Trajectory-based 3-d games of chance for video gaming machines

ABSTRACT

Trajectory-based games of chance are described that may be implemented on a video gaming machine. In a trajectory-based game of chance, a trajectory of a game object may be generated in a 3-D gaming environment. A wager may be made on an aspect of the game object&#39;s trajectory in the gaming environment such as a termination location for the trajectory of the game object. The aspect of the game object&#39;s trajectory may occur according to a known probability. Hence, an award for the trajectory-based game of chance may be proportional to the probability of the aspect of the game object&#39;s trajectory occurring.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a divisional application of co-pending U.S.patent application Ser. No. 10/187,343, filed on Jun. 27, 2002, and isrelated to U.S. application Ser. No. 09/553,438, filed on Apr. 19, 2000,now U.S. Pat. No. 6,769,982 titled, “Video Pachinko On A Video PlatformAs A Gaming Device”, and U.S. application Ser. No. 09/927,901, filedAug. 9, 2001, now U.S. Pat. No. 6,887,157, titled, “Virtual Cameras And3-D Gaming Environments In A Gaming Machine,” each of which areincorporated herein by reference in their entirety for all purposes.

BACKGROUND OF THE INVENTION

This invention relates to game playing methods for gaming machines suchas slot machines and video poker machines. More particularly, thepresent invention relates to methods of allowing game players to playtrajectory-based games of chance on a video gaming machine.

There are a wide variety of devices that can comprise a gaming machinesuch as a slot machine or video poker machine. Some examples of thesedevices are lights, slot reels, ticket printers, card readers, speakers,bill validators, coin acceptors, display panels, key pads, bonus wheels,and button pads. These devices provide many of the features which allowa gaming machine to present a game. Some of these devices are built intothe gaming machine. Often, a number of devices are grouped together in aseparate box that is placed on top of the gaming machine. Devices ofthis type are commonly called a top box.

Typically, utilizing a master gaming controller, the gaming machinecontrols various combinations of devices that allow a player to play agame of chance on the gaming machine and also encourage game play on thegaming machine. For example, a game played on a gaming machine usuallyrequires a player to input money or indicia of credit into the gamingmachine, indicate a wager amount, and initiate a game play. These stepsrequire the gaming machine to operate input devices including billvalidators and coin acceptors to accept money into the gaming machineand recognize user inputs from devices including key pads and buttonpads to determine the wager amount and initiate game play.

After a game of chance has been initiated on the gaming machine, thegaming machine determines a game outcome and presents the outcome of thegame to a player. For example, for a slot game, after a player hasinitiated a game by pressing an input button or pulling a handleattached to the gaming machine, the gaming machine determines a gameoutcome which is the final position of each reel on the slot machine. Arequirement for most gaming machines is that the probability of eachgame outcome is precisely known and remains constant during game play.Thus, when a player plays two or more games on a gaming machine theprobability of a particular game outcome is the same for each game thatthe player initiates.

After the gaming machine determines the game outcome, the outcome of thegame is presented to the player. For the slot game, the game outcomepresentation might include a number reels spinning, visual effectsincluding flashing or strobing lights and auditory effects includingbells and whistles. The game outcome presentation, including the variousvisual and auditory effects, is designed to add excitement to the gamebeing played on the gaming machine and encourage additional game play.

Usually near the end of the game outcome presentation, the game outcomeis presented. For example, for the slot game, the reels stop at a finalposition. Based on the game outcome, the gaming machine may notify theplayer of an award of a varying amount or notify the player that thewager made on the game was lost. For example, for a slot game with threeslot reels, when the final position of each reel corresponds to thedisplay of an identical symbol including three cherries, three bars orthe like, a player might be awarded a credit of 5 times the initialwager made on the game. However, other symbol combinations including 2cherries and a bar or two bars and a cherry might result in a loss ofthe wager made on the game. Further, each time a player plays a game theprobability of a particular game outcome such as three cherries or threebars will usually be the same. After the game outcome has beenpresented, a player may initiate a new game by making a new wager on thegaming machine and initiating the next game play.

In addition to the game of chance on the gaming machine on the gamingmachine, a player may also be presented a bonus game. The bonus game maybe used to add additional excitement to the play of games on the gamingmachine. In bonus games, which are particular popular with video slotgames, the player is offered the chance to win an additional awardamount. The bonus game may be triggered by different events that occurduring the play of the game of chance. For instance, in a slot game, aparticular symbol or combination of symbols appearing on the reels maytrigger the bonus game.

The bonus game may incorporate additional animations that are displayedon one or more video displays on the gaming machine and the activationof one or more peripheral devices associated with the gaming machine.For example, Wheel-of-Fortune™ by IGT (Reno, Nev.) is a very popularbonus game that incorporates a large spinning wheel attached to thegaming machine. When the bonus game is triggered, the wheel spins up.The bonus may be awarded according to the stopping place of the wheel.

The amount of game play on a gaming machine is usually a function of thetype of game of chance. A few examples of games that are played on videogaming machines are slot games, poker, blackjack, and keno. Among thesegames, slot games and video poker are probably the most popular. Thetype of bonus games offered with the game of chance may also influencethe popularity of a particular game. A casino typically offers varioustypes of games and bonus games because many game players are attractedto some games but dislike others. When a player wants to play a game ona gaming machine but does not like any of the offered games, this personmay choose not to play. Also, when a player finds a particular game onlymildly exciting, the player may become disinterested after a short timeand cease their game play. Thus, to increase game play, new games ofchance and bonus games are desired that may attract players previouslyuninterested in game play on a gaming machine. Accordingly, to attractnew players, new games for gaming machines are desired that are excitingand are interesting enough to hold a player's interest over a longperiod of time.

SUMMARY OF THE INVENTION

This invention addresses the needs indicated above by providing a gamingmachine on which a trajectory-based game of chance may be played. In atrajectory-based game of chance, a trajectory of a game object may begenerated in a 3-D gaming environment. A sequence of 2-D images thatshow the game object's trajectory may be rendered for the 3-D gamingenvironment and displayed on a display screen on the gaming machine aspart of a game outcome presentation for the trajectory-based game ofchance. A wager may be made on an aspect of the game object's trajectoryin the gaming environment such as a termination location for thetrajectory of the game object. The aspect of the game object'strajectory may occur according to a known probability. Hence, an awardfor the trajectory-based game of chance may be proportional to theprobability of the aspect of the game object's trajectory occurring.

The first two aspects of the present invention provide methods ofgenerating trajectory-based game of chance on a gaming machine. Thefirst method may be generally characterized as comprising: 1) receivinga request to initiate a trajectory-based game of chance; 2) determininga game outcome for the trajectory-based game of chance; 3) after thegame outcome has been determined, generating a trajectory of athree-dimensional (3-D) game object in a 3-D gaming environment thatcorresponds to the determined game outcome; and 4) displaying as part ofa game outcome presentation for the trajectory-based game of chance asequence of two-dimensional images rendered from the 3-D gamingenvironment to a display screen on the gaming machine wherein thesequence of two-dimensional images comprise one or more two-dimensionalimages of the 3-D game object along its trajectory in the 3-D gamingenvironment.

In particular embodiments of the first method, two or moretrajectory-based games of chance may be played in parallel. Forinstance, the first method may further comprise: a) prior to displayingthe game outcome for the trajectory-based game of chance, receiving arequest to initiate a second trajectory-based game of chance b)determining a game outcome for the second trajectory-based game ofchance; c) after the game outcome has been determined for the secondtrajectory-based game of chance, generating a trajectory of a secondthree-dimensional (3-D) game object in the 3-D gaming environment thatcorresponds to the determined game outcome of second trajectory-basedgame of chance; and e) displaying, as part of a game outcomepresentation for the trajectory-based game of chance and the secondtrajectory-based game of chance, a sequence of two-dimensional imagesrendered from the 3-D gaming environment to the display screen on thegaming machine where the sequence of two-dimensional images comprise oneor more two-dimensional images with both the 3-D game object along itstrajectory in the 3-D gaming environment and the second 3-D game objectalong its trajectory in the 3-D gaming environment. Further, the methodmay comprise receiving a first wager for the trajectory-based game ofchance and receiving a second wager separate from the first wager forthe second trajectory-based game of chance. In some embodiments, thegame outcome for the second trajectory-based game of chance may beindependent of the trajectory-based game of chance. In otherembodiments, the game outcome for the second trajectory-based game ofchance may be dependent on the trajectory-based game of chance.

As another example, the first method may further comprise: i) generatinggame outcomes for a plurality of trajectory-based games of chances wherea separate wager is made on each of the plurality of trajectory-basedgames of chance; ii) generating a trajectory of a three-dimensional(3-D) game object in a 3-D gaming environment that corresponds to thedetermined game outcome for each of the plurality of trajectory-basedgames of chance; iii) displaying, as part of a game outcomepresentations for the plurality of trajectory-based games of chance, atleast one sequence of two-dimensional images rendered from the 3-Dgaming environment to the display screen on the gaming machine where theat least one sequence of two-dimensional images comprise one or moretwo-dimensional images with two or more of the 3-D game objects alongtheir trajectory in the 3-D gaming environment.

The second aspect of the present invention provides a second method ofgenerating a trajectory-based game of chance on a gaming machine. Themethod may be generally characterized as comprising: 1) receiving arequest to initiate a trajectory-based game of chance; 2) generating atrajectory of a three-dimensional (3D) game object in a 3-D gamingenvironment; 3) determining a game outcome for the trajectory-based gameof chance wherein the game outcome is not determined until the 3-D gameobject reaches a final state of its trajectory in the 3-D gamingenvironment; and 4) displaying, as part of a game outcome presentationfor the trajectory-based game of chance, a sequence of two-dimensionalimages rendered from the 3-D gaming environment to a display screen onthe gaming machine where the sequence of two-dimensional images compriseone or more two-dimensional images of the 3-D game object along itstrajectory in the 3-D gaming environment. In one embodiment, for thetrajectory-based game of chance, the game outcome may be independent ofthe trajectory of the 3-D game object in the 3-D gaming environment.

In another embodiment, the game outcome for the trajectory-based game ofchance may be based-upon the final state of the trajectory in the 3-Dgaming environment. In the second method, two or more trajectory-basedgames of chance may be played in parallel.

The following embodiments of the present invention may be used witheither the first method or the second method for generating thetrajectory-based game of chance. The trajectory-based game of chance maybe a pachinko game. The 3-D game object may be a sphere or a polyhedronand the trajectory of the 3-D game object may be a planar trajectory.The 3-D gaming environment may comprise data and/or instructions forgenerating: i) a plurality of 3-D objects; ii) a plurality of trajectoryrules for determining the trajectory of a moving 3-D object in the 3-Dgaming environment; iii) a plurality of collision rules for determiningeffects of a collision between 3-D objects in the 3-D gamingenvironment; and a plurality of exit rules for removing the 3-D gameobject from the 3-D gaming environment. The 3-D gaming environment mayalso comprise data and/or instructions for generating a plurality ofgame levels for the trajectory-based game of chance.

In other embodiments, the methods for generating the trajectory-basedgame of chance may comprise one or more of the following: a) changingthe geometry of the 3-D game object along its trajectory, b) receiving awager for the trajectory-based game of chance, c) selecting an initialstate for the 3-D game object in 3-D gaming environment where theinitial state provides initial conditions for the trajectory of the 3-Dgame object in the 3-D gaming environment (The initial state maycomprise an initial position of the 3-D game object in the 3-D gamingenvironment and an initial velocity of the 3-D game object in the 3-Dgame object.), d) displaying the game outcome for the trajectory-basedgame of chance and redisplaying one or more two-dimensional images ofthe 3-D game object along its trajectory and e) removing the 3-D gameobject from the 3-D gaming environment.

In another embodiment, the methods may also comprise receiving an outputsignal from a user interface for the trajectory-based game of chance andusing information from the output signal, selecting an initial state forthe 3-D game object in the 3-D gaming environment wherein the initialstate provides initial conditions for the trajectory of the 3-D gameobject in the 3-D gaming environment. The user interface may comprise a)a plunger; and b) one or more sensors wherein the one or more sensorsare designed to generate an output signal with information indicating atleast one i) an amount of force applied to the plunger, ii) an actuationof the plunger has been initiated and iii) combinations thereof.

In yet another embodiment of the methods, a virtual camera may be usedin the 3-D gaming environment to render the two-dimensional images usedas part of a game outcome presentation. A position of a virtual camerafor rendering images in the sequence of two-dimensional images changesas a function of time. Further, a virtual camera for rendering images inthe sequence of two-dimensional images is located on the 3-D game objectand travels with the 3-D game object along its trajectory. In addition,two or more virtual cameras in the 3-D gaming environment may be used torender images in the sequence of two-dimensional images. The methods maycomprise one or more of the following: i) receiving an output signalfrom an input device on the gaming machine where the output signalincludes information used to change a position of a virtual camera forrendering images in the sequence of two-dimensional images and ii)receiving an output signal from an input device on the gaming machinewherein the output signal includes information used to select a virtualcamera for rendering images in the sequence of two-dimensional images.

In additional embodiments, the two methods for generating atrajectory-based game of chance may comprise detecting a collisionbetween the 3-D game object and a second 3-D object in the 3-D gamingenvironment. The second 3-D object may be a second 3-D game object. Inresponse to the collision between the 3-D game object and the secondobject, the methods may comprise one or more of the following: a)modifying the trajectory of the 3-D game object, b) generating a bonusgame for the trajectory based game of chance, c) modifying a property ofthe 3-D game object and d) generating a game event. The methods may alsocomprise detecting an intersection of the 3-D game object with a surfacein the 3-D gaming environment. In response to detecting theintersection, the methods may comprise one or more of the following: i)terminating the trajectory of the 3-D game object, ii) transporting the3-D game object to a location in the 3-D gaming environment away from alocation of the intersection, iii) modifying a property of the 3-D gameobject, iv) starting a bonus game, and v) triggering a game event.

Another aspect of the present invention provides a method of generatinga pay-table for a trajectory-based game of chance. The method may begenerally characterized as comprising: 1) inserting a plurality of 3-Dgame objects into a 3-D gaming environment wherein each of the pluralityof 3-D game objects is assigned an initial state; 2) generating atrajectory for each of the 3-D game objects in the 3-D gamingenvironment, the trajectory of each 3-D game object comprising: theinitial state in the 3-D gaming environment, a final state in the 3-Dgaming environment, and one or more states in the 3-D gaming environmentbetween the initial state and the final state; 3) assigning a gameoutcome for the trajectory-based game of chance from a set of gameoutcomes to the final state of each 3-D game object in the 3-D gamingenvironment; and 4) generating a pay table that relates each gameoutcome in the set of game outcomes to a probability of that gameoutcome occurring.

In particular embodiments, the initial state may comprise an initialposition and an initial velocity. The trajectory for each of the 3-Dgame objects may be planar. The trajectory-based game of chance may be apachinko game. The 3-D game object may be a sphere or a polyhedron.

The method may also comprise one or more of the following: a) installingthe paytable on a gaming machine and generating game outcomes for aplurality of trajectory-based games of chance using the paytable, b)generating a set of game outcomes, c) generating a trajectory table thatrelates each game outcome in the set of game outcomes to one or moredifferent initial states wherein each of the one or more differentinitial states is for generating a trajectory corresponding to itsrelated game outcome and d) installing the paytable, the 3-D gamingenvironment and the trajectory table on a gaming machine; on the gamingmachine, generating a first game outcome using the pay table; selectingan initial state for the first game outcome using the trajectory table;and generating in the 3-D gaming environment a first trajectorycorresponding to the first game outcome using the initial state selectedfrom the trajectory table. The method may also comprise generating the3-D gaming environment for the trajectory-based game of chance. The 3-Dgaming environment may comprise data and/or instructions for generating;a plurality of 3-D objects; a plurality of trajectory rules fordetermining the trajectory of a moving 3-D object in the 3-D gamingenvironment; a plurality of collision rules for determining effects of acollision between 3-D objects in the 3-D gaming environment; and aplurality of exit rules for removing the 3-D game object from the 3-Dgaming environment.

Another aspect of the present invention provides a method of generatinga game outcome presentation in a trajectory-based game of chance. Themethod may be generally characterized as comprising: 1) along atrajectory of a 3-D game object in a 3-D gaming environment wherein thetrajectory comprises a sequence of states of the 3-D game object in the3-D gaming environment and wherein each states comprises at least aposition and a velocity of the 3-D game object; generating a first statein the sequence of states of the 3-D game object along its trajectory;and 2) generating a second state in the sequence of states of the 3-Dgame object along its trajectory that is related to the first state by aplurality of trajectory rules; where one or more two-dimensional imagesare rendered of the 3-D game object along its trajectory in the 3-Dgaming environment as part of the game outcome presentation for thetrajectory-based game of chance.

In particular embodiments, the trajectory rules may simulate one or moreof gravitational forces, frictional forces and environmental forces onthe 3-D game object. The velocity of the 3-D game object along itstrajectory may be planar. Further, the velocity of the 3-D game objectalong its trajectory may comprise one or more of translational velocitycomponents, rotational velocity components, vibrational velocitycomponents and combinations thereof. The plurality of trajectory rulesmay be determined at each location in the 3-D gaming environment.Therefore, a plurality of trajectory rules at a first location in the3-D gaming environment may be different than a plurality of trajectoryrules at a second location in the 3-D gaming environment. Thetrajectory-based game of chance may be a pachinko game. The 3-D gameobject may be a sphere or a polyhedron.

The method may further comprise one or more of the following: a)determining a game outcome for the trajectory-based game of chance;looking up in an initial position and an initial velocity of the 3-Dgame object in a trajectory table that corresponds to the determinedgame outcome and assigning the initial position and the initial positionof the 3-D game object to the first state, b) after generating aposition and a velocity of the 3-D game object at the second state,assigning the position and the velocity of the 3-D game object at thesecond state to the first state and generating a new second state, d)determining that the 3-D game object has exited the 3-D gamingenvironment between the first state and the second state; removing the3-D game object from the 3-D gaming environment; and displaying the gameoutcome for the 3-D game object, and e) determining the plurality oftrajectory rules that are used to relate the first state to the secondstate.

In another embodiment, the method may further comprise detecting anintersection of the 3-D game object with a surface in the 3-D gamingenvironment between the first state and the second state. In response todetecting the intersection, the method may comprise one or more of thefollowing: a) terminating the trajectory of the 3-D game object andremoving the 3-D game object from the 3-D gaming environment, b)generating a new position for the second state different from theposition of the second state wherein the 3-D game object appears to movediscontinuously from the first state to the second state (The newposition may be located in a bonus area of the 3-D gaming environment.),c) modifying a property of the 3-D game object where the property of the3-D game object that is modified is selected from the group consistingof a mass property, a geometry property, a graphical rendering property,a sound property and a bonus property, d) modifying a property of anobject in the 3-D gaming environment, e) triggering a bonus game, f)triggering a game event, g) splitting the 3-D game object into aplurality of 3-D game objects and h) modifying a velocity component ofthe 3-D game object where the velocity component is selected from thegroup consisting of a translational velocity component, a rotationalvelocity component and a vibrational velocity component.

In another embodiment, the method may comprise: after generating thesecond state, between the first state and the second state, detecting acollision between the 3-D game object and a second object in the 3-Dgaming environment. The second object may be a second game object. Inresponse to detecting the collision, the method may comprise one or moreof the following: i) generating an pre-collision state for the 3-D gameobject and the second object; generating a post-collision state for the3-D game object and the second object wherein the pre-collision stateand the post collision state are related by a plurality of collisionrules; and assigning the post-collision state for the 3-D game object tothe second state, ii) determining the plurality of collision rules thatare used to determine effects of the collision between the 3-D gameobject and the second game object which may vary from location tolocation in the 3-D gaming environment and from object to object, iii)modifying a property of the 3-D game object where the property of the3-D game object that is modified is selected from the group consistingof a mass property, a geometry property, a graphical rendering property,a sound property and a bonus property, iv) modifying a property of thesecond object where the property of the second object that is modifiedis selected from the group consisting of a mass property, a geometryproperty, a graphical rendering property, a sound property and a bonusproperty, v) triggering a bonus game, vi) triggering a game event in thetrajectory based game of chance, vii) splitting the 3-D game object intoa plurality of 3-D game objects, viii) terminating the trajectory of the3-D game object and removing the 3-D game object from the 3-D gamingenvironment.

Another aspect of the present invention provides a gaming machine. Thegaming machine may be generally characterized as comprising: 1) a mastergaming controller designed or configured i) to control a game of chanceplayed on the gaming machine, ii) to generate a trajectory of a 3-D gameobject in a 3-D gaming environment used in a trajectory-based game ofchance, iii) to render a sequence of two-dimensional images from the 3-Dgaming environment wherein the sequence of two-dimensional imagescomprises one or more two-dimensional images of the 3-D game objectalong its trajectory and iv) to generate a game outcome for thetrajectory-based game of chance; and 2) a video display for displayingthe sequence of two-dimensional images as part of a game outcomepresentation for the trajectory-based game of chance. The gaming machinemay further comprise a sound projection device wherein the soundprojection device is used to at least emit sounds in response tocollisions between the 3-D game object and 3-D objects along itstrajectory in the 3-D gaming environment.

In particular embodiments, the trajectory-based game of chance may be apachinko game. Further, the game of chance controlled by the gamingmachine may be selected from the group consisting of a slot game, a kenogame, a poker game, a pachinko game, a black jack game, a bingo game, abaccarat game, a roulette game, a dice game, a card game and atrajectory based game of chance. The 3-D game object may be a sphere ora polyhedron. The trajectory of the 3-D game object may be planar. Aplurality of trajectory-based games of chance may be played in parallel.The sequence of images rendered from the 3-D gaming environment may bedisplayed simultaneously on a plurality of displays.

In another embodiment, the gaming machine may further comprise: a memorystorage device for storing at least one of i) instructions, ii) data andiii) combinations thereof for generating the 3-D gaming environment. The3-D gaming environment may comprise data and/or instructions forgenerating: a) a plurality of 3-D objects; b) a plurality of trajectoryrules for determining the trajectory of a moving 3-D object in the 3-Dgaming environment; c) a plurality of collision rules for determiningeffects of a collision between 3-D objects in the 3-D gamingenvironment; and d) a plurality of exit rules for removing the 3-D gameobject from the 3-D gaming environment. The gaming machine may alsocomprise a memory storage device for storing a pay table for thetrajectory-based game of chance and a memory storage device for storinga trajectory table for the trajectory-based game of chance where thetrajectory table contains data that relates one or more initialtrajectory states for the 3-D game object to the game outcome for thetrajectory based game of chance. A single memory storage device ormultiple memory storage devices may be used to store the 3-D gamingenvironment, the pay-table and the trajectory table.

In yet another embodiment, the gaming machine may further comprise auser interface for the trajectory-based game of chance. The userinterface may comprise: 1) a first input device; and 2) one or moresensors connected to the first input device used to detect anoperational parameter of the input device and generate an output signalcorresponding to the operational parameter wherein the output signal isused to at least one of i) to initiate the trajectory-based game ofchance, ii) to generate an initial state of the 3-D object for itstrajectory in the 3-D gaming environment, and iii) combinations thereof.The first input device may be a plunger where the one or more sensorsare designed to generate an output signal with information indicating atleast one of i) an amount of force applied to the plunger, ii) anactuation of the plunger has been initiated and iii) combinationsthereof. The first input device may also be a touch screen display wherethe one or more sensors are touch screen sensors. The touch screensensors may generate an output signal with information indicating aselected amount of force displayed on the touch screen display.

Further, the user interface may comprise: a) a ball; b) a ball conduitfor the ball; and c) one or more sensors designed to measure a positionof the ball along the ball conduit where the plunger is designed tostrike the ball at an initial position on the ball conduit such that theball is propelled along the ball conduit away from its initial positionand where the ball conduit is designed to return the sphere to theinitial position on the ball conduit. The user interface may comprise asound projection device where the sound projection device emits a soundin response to the plunger striking the ball. The volume of the soundmay be proportional to the force applied to the plunger. The userinterface may also comprise a light panel comprising a plurality oflights where a number of lights are lit on the light panel in proportionto the amount of force applied to the plunger. The user interface maycomprise a graphical force meter on the display screen where the amountof force applied to the plunger is displayed on the graphical forcemeter.

In another embodiment, the user interface may further comprise a secondinput device where the second input device is for selecting a rate atwhich a plurality of trajectory-based games of chance are automaticallyinitiated. The second input device may be a touch screen display or acontrol knob where a position of the control knob is used to select therate at which a plurality of trajectory-based games of chance areautomatically initiated. The user interface may comprise an additionalinput device where the additional input device is for selecting a wageramount for each of a plurality of trajectory-based games of chance.Again, the second input device may be a touch screen display. The userinterface may comprise an additional input device where the additionalinput device is for selecting one or more of a shape of the 3-D gameobject, a property of the 3-D game object and a property of the 3-Dgaming environment. Once again, the second input device may be a touchscreen display.

Another aspect of the present invention provides a product comprising atleast one of i) data, ii) instructions and iii) combinations thereof forrepresenting a 3-D gaming environment for a trajectory-based game ofchance. The 3-D gaming environment being provided on a computer readablemedium and comprising data and/or instructions for generating: 1) aplurality of 3-D objects; 2) a plurality of trajectory rules that areused to determine the trajectory of a moving 3-D object in the 3-Dgaming environment; 3) a plurality of collision rules that are used todetermine effects of a collision between 3-D objects in the 3-D gamingenvironment; and 4) a plurality of exit rules that are used to removethe moving 3-D object from the 3-D gaming environment where the 3-Dgaming environment is for rendering a sequence of two-dimensional imagesthat are used as part of a game outcome presentation for thetrajectory-based game of chance. The 3-D gaming environment may comprisea plurality of game levels. The trajectory rules may be defined at eachlocation in the 3-D gaming environment where the trajectory rules at afirst location are different than the trajectory rules at a secondlocation in the 3-D gaming environment. The 3-D gaming environment maycomprise one or more bonus areas that are for rendering a bonus gamepresentation.

Another aspect of the present invention provides a user interface for agaming machine. The user interface may be generally characterized ascomprising: 1) an input device; and 2) a sensor connected to the inputdevice used to detect an operational parameter of the input device andgenerate an output signal corresponding to the operational parameterwherein the output signal is used to at least one of i) to initiate atrajectory-based game of chance, ii) to generate an initial state of a3-D game object for its trajectory in a 3-D gaming environment, and iii)combinations thereof where the 3-D gaming environment is for rendering asequence of two-dimensional images that are used as part of a gameoutcome presentation for the trajectory-based game of chance. Thetrajectory-based game of chance may be a pachinko game.

In particular, the first input device may be a plunger where the one ormore sensors are designed to generate an output signal with informationindicating at least one of i) an amount of force applied to the plunger,ii) an actuation of the plunger has been initiated and iii) combinationsthereof. The user interface with the plunger may also comprise: a) aball; b) a ball conduit for the ball; c) and one or more sensorsdesigned to measure a position of the ball along the ball conduit wherethe plunger is designed to strike the ball at an initial position on theball conduit such that the ball is propelled along the ball conduit awayfrom its initial position and wherein the ball conduit is designed toreturn the ball to the initial position on the ball conduit. The userinterface with the plunger and the ball may also comprise a soundprojection device wherein the sound projection device emits a sound inresponse to the plunger striking the ball. The volume of the sound isproportional to the force applied to the plunger which may be measuredby one or more sensors. The user interface with the plunger may alsocomprise a light panel comprising a plurality of lights wherein a numberof lights are lit on the light panel in proportion to the amount offorce applied to the plunger.

Another aspect of the invention pertains to computer program productsincluding a machine-readable medium on which is stored programinstructions for implementing any of the methods described above. Any ofthe methods of this invention may be represented as program instructionsand/or data structures, databases, etc. that can be provided on suchcomputer readable media.

These and other features of the present invention will be presented inmore detail in the following detailed description of the invention andthe associated figures.

FIG. 1A is a perspective drawing of a plurality of trajectories for gameobjects in a 3-D gaming environment.

FIG. 1B is a block diagram describing trajectory rules and collisionrules for two objects in the 3-D gaming environment described withrespect to FIG. 1A.

FIG. 2 is a flow chart depicting a method of generating a trajectory fora game object in a 3-D gaming environment.

FIG. 3 is a flow chart depicting a method of generating a pay-table fora trajectory-based game of chance.

FIG. 4 is a flow chart depicting a first method of generating atrajectory-based game of chance on a gaming machine.

FIG. 5 is a flow chart depicting a second method of generating atrajectory-based game of chance on a gaming machine.

FIG. 6 is a block diagram of a gaming environment where the physicalproperties vary as a function of space and time.

FIG. 7 is a block diagram used to described bonusing methods for a 3-Dtrajectory-based game of chance.

FIG. 8 is a perspective drawing of a 3-D gaming environment implementedon a gaming machine for one embodiment of this invention.

FIG. 9 is a block diagram depicting a hardware interface for a 3-Dtrajectory based game of chance.

FIG. 10 is a perspective drawing of a gaming machine for one embodimentof the present invention.

FIG. 11 is a block diagram of a gaming network for one embodiment of thepresent invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

In the present invention, trajectory-based games of chance are describedthat may be implemented on a video gaming machine. In a trajectory-basedgame of chance, a trajectory of a game object may be generated in a 3-Dgaming environment. A wager may be made on an aspect of the gameobject's trajectory in the gaming environment such as a terminationlocation for the trajectory of the game object. The aspect of the gameobject's trajectory may occur according to a known probability. Hence,an award for the trajectory-based game of chance may be proportional tothe probability of the aspect of the game object's trajectory occurring.

As an example, the gaming environment may be designed with one hundredexits where the trajectory of the game object always ends in one of ahundred of exits in the gaming environment and where there is an equalprobability of the game object landing in a particular exit. The gameobject may be a sphere. A wager for this trajectory-based game of chancemay be based upon the exit where the sphere lands at the end of itstrajectory. Therefore, the aspect of the trajectory for which the wageris made is the final state of the sphere's trajectory. The award forthis trajectory-based game of chance may be even money where the spherelanding in one of 49 of the exits results in an award and where thesphere landing in one of 51 of the exits results in no award and a lossof the wager.

The gaming environment may be a simulation implemented on a computingdevice on the gaming machine. The gaming environment may comprise dataand/or instructions for generating: 1) objects and their properties thatare located in the gaming environment, 2) trajectory rules fordetermining the trajectory of the game object and other objects in thegaming environment, 3) collision rules for determining effects of acollision between objects in the gaming environment and 4) exit rulesfor determining when the game object or other objects are removed fromthe gaming environment.

A game sequence for the trajectory-based game of chance played on agaming machine by a player may consist of the following steps by theplayer and the gaming machine 1) make wager (player), 2) initiate game(player), 3) determine game outcome (gaming machine) and 4) generategame outcome presentation (gaming machine). The game outcome may bedetermined before or after the game outcome presentation is generated.As part of the game outcome presentation, the trajectory of game objectin the gaming environment is generated by the gaming machine and ispresented to the player on one or more display screens on the gamingmachine. Besides the visual display of the game object's trajectory, thegame outcome presentation may include additional visual effects, audioeffects and other effects designed to stimulate a player's senses thatare generated on the gaming machine interface. In general, the format ofthe game outcome presentation is designed to at least allow the playerto view the aspect of the trajectory upon which an award for thetrajectory-based game of chance is based. For instance, in the exampledescribed above where a spherical game object travels through the gamingenvironment and exits through one of a hundred exits, the game outcomepresentation may comprise displaying the sphere along its trajectory inthe gaming environment until it leaves the gaming environment throughone of the exits. The exits may be labeled so that the player candetermine whether they have won an award.

In FIG. 1A, general aspects of a gaming environment and a game object'strajectory in the gaming environment for a trajectory-based game ofchance are described. In FIG. 1B, simulation techniques for generatingthe trajectory of a game object are discussed. In FIG. 2, a method ofgenerating the trajectory for the game object is described. In FIG. 3, amethod of generating a paytable for the trajectory-based game of chanceis described. In FIGS. 4 and 5, two methods of generating thetrajectory-based game of chance on a gaming machine are described. InFIG. 6, trajectory rules for the gaming environment that may varyaccording to time and location are described. In FIG. 7, bonus games fortrajectory-based games of chance are described. In FIG. 8, details ofmethods of rendering 2-D images from a 3-D gaming environment used forthe trajectory-based game of chance are described. In FIG. 9, mechanicalinterfaces for trajectory-based games of chance on a gaming machine aredescribed. In FIGS. 10 and 11, gaming machines and a gaming machinenetwork that may be used with trajectory-based games of chance aredescribed.

In one embodiment of the present invention, the gaming environment andthe game objects may be generated in 3-D dimensions. To generate a gameoutcome presentation, a sequence of 2-D images may be rendered from the3-D gaming environment using a virtual camera. The 3-D gamingenvironment 300 may comprise data and/or instructions for generating: 1)a plurality of 3-D objects; 2) a plurality of trajectory rules that areused to determine the trajectory of a moving 3-D object in the 3-Dgaming environment; 3) a plurality of collision rules that are used todetermine effects of a collision between 3-D objects in the 3-D gamingenvironment; and 4) a plurality of exit rules that are used to removethe moving 3-D object.

The 3-D gaming environment 300 may be comprised of a plurality of 3-Dobjects and surfaces. For example, in FIG. 1A, the 3-D gamingenvironment is comprised of a number of rectangular boxes and two solidplanar surfaces with holes. The upper planar surface has three holes andthe lower planar surface has four holes. The 3-D objects are defined ina rectangular coordinate system 304 with x, y, and z directions.

When a 3-D gaming environment 300 is generated, a number of 3-Dobjects/surfaces in the 3-D gaming environment, a location of 3-Dobjects/surfaces in the 3-D gaming environment and a shape of 3-Dobjects in the 3-D gaming environment 300 may be varied and is notlimited to the example in FIG. 1A. The shapes of 3-D objects modeled inthe 3-D gaming environment may be simple or complex. For instance, therectangular boxes, spheres (e.g., 320, 322, 326, 330), diamond 332 andpyramid 333 are examples of simple shapes. Multi-dimensional models ofpeople, buildings, landscapes and casino interiors are examples ofcomplex objects that may be modeled in a 3-D gaming environment. Furtherdetails of modeling 3-D objects in the present invention are describedwith respect to FIG. 8.

The 3-D gaming environment may incorporate various themes andbackgrounds. For instance, one theme and background may relate to acitiscape where the game objects used in the trajectory-based game ofchance are launched into the city. In one embodiment, the player may beable to select backgrounds and gaming environments that correspond todifferent cities, such as Paris, New York and London. The gamingenvironment for each city may include objects that model buildings ineach city.

The rectangular boxes are shown at fixed locations in the 3-D gamingenvironment 300. A position of 3-D objects in the 3-D gamingenvironment, such as the rectangular boxes may vary. For instance, oneor more of the boxes may move around the gaming environment and collidewith other 3-D objects in the gaming environment. Translational,rotational and vibrational velocities of 3-D objects may be simulated inthe 3-D gaming environment. Further, different 3-D objects may besimulated with different combinations of these velocity components. Forinstance, some 3-D objects may translate around the gaming environmentwithout rotating or vibrating while other 3-D objects may rotate orvibrate in place without translating.

The 3-D gaming environment may include a number of exits that are usedto terminate the trajectory of an object and remove the object from theenvironment. In general, the exits in the gaming environment are notbased upon location but based upon exit rules. The exit rules define aset of conditions that are used to determine when the trajectory of amoving object is terminated and the object is removed from the gamingenvironment. For example, the opening 354 in the first planar surface329, and the four openings, 334, 353, 355 and 356, in the second planarsurface, 352, may be used as exits for the gaming environment 300. Anexit rule for these openings may be that when any object intersects asurface defining a mouth to the opening, then the trajectory of theobject is terminated and the object is removed from the gamingenvironment 300. Another exit rule for the openings may be that onlyobjects with a particular set of properties are removed when the objectintersects the surface defining the mouth to the opening. For otherobjects without the required properties, the opening acts as a solid.For example, a spherical-shaped object that intersect the opening 354may be removed the gaming environment while a diamond-shaped objects maybounce off of the opening 354.

The specification of exit rules may be considered part of the design ofthe gaming environment 300. Many different combinations of exit rulesmay be defined in the gaming environment 300. Further, the exit rulesmay vary as a function of time and from location to location in thegaming environment. Additional examples of exit rules that may be usedwith the present invention are as follows. One exit rule may be thatwhen a moving object collides with a particular object the trajectory ofthe moving object is terminated and the moving object is removed fromthe gaming environment. In other embodiments, the exit rule may be thatan object is removed from the gaming environment after one or more ofthe following: 1) after an amount of time, 2) after a number ofcollisions, 3) at random, 4) after a distance traveled along ittrajectory, 5) after passing a velocity threshold, such as a maximumvelocity or minimum velocity, and 6) combinations thereof.

The 3-D gaming environment may be generated with a plurality of gamelevels and/or regions with entrances connecting the levels or theregions. For example, a space above a first planar surface 329 may beused as a first game level in the trajectory-based game of chance. Thespace between the first planar surface 329 and the second planar surface352 may be used as a second game level in the trajectory-based game ofchance. The two openings in the first planar surface, 323 and 331, maybe used to connect the first game level and the second game level.

In one embodiment, an opening may be used to transfer objects to a bonusspace in the 3-D gaming environment. For instance, an object that passesthrough the opening 354 may be transferred to a bonus space modeled inthe 3-D gaming environment. In another embodiment, a plurality of 3-Dgaming environments may be modeled on the gaming machine. Therefore, anobject that passes through one of the openings may be transferred toanother 3-D gaming environment. In yet another embodiment, different 3-Dgaming environments may be modeled on a plurality of different linkedgaming machines and objects may be transferred between the gamingenvironments generated on different gaming machines. In addition, aplurality of linked gaming machines may share a common gamingenvironment. In the common 3-D gaming environment, trajectory-basedgames of chance may be initiated from each of the linked gaming machinesin the 3-D gaming environment. On each gaming machine, 2-D imagesrendered from the shared gaming environment may be used in a gameoutcome presentation for trajectory-based game of chance initiated fromthat gaming machine. On a first gaming machine, the 2-D images may showone or more game objects used in trajectory-based games of chanceinitiated on gaming machines different than the first gaming machine.

As described above, in the trajectory-based game of chance, a wager maybe made on an aspect of a 3-D game object's trajectory in the 3-D gamingenvironment. Typically, during its trajectory, the 3-D game objectcollides with many different combinations of objects before reaching afinal state in its trajectory and being removed from the gamingenvironment, such as leaving the 3-D gaming environment through an exit.During the game outcome presentation, the interaction of the 3-D gameobject with various objects in the 3-D gaming environment 300 along itstrajectory and the uncertainty of the final destination of the 3-D gameobject adds to the excitement of the trajectory-based game of chance.

Some examples of aspects of the trajectory of the game object that maybe used to provide a basis for a wager are as follows. A wager may bemade upon: 1) an exit that the game object leaves the gamingenvironment, 2) a number of collisions between the game object and otherobjects along its trajectory, 3) a length of time for the trajectory, 4)a distance traveled by the game object along its trajectory, 5) a finallocation of the game object, 6) a final velocity of the game object and7) combinations thereof. The present invention, however, is not limitedto these examples.

After a wager has been made and the trajectory-based game of chance hasbeen initiated, a 3-D game object with an initial state may beintroduced into the 3-D gaming environment 300. The initial state of the3-D game object may comprise information about a number of propertiesabout the game object including but not limited to 1) an initialposition in the coordinate system, 2) an initial velocity which mayinclude a translational velocity, a rotational velocity, a vibrationalvelocity and combinations thereof, 3) mass properties, 4) a geometry, 5)physical properties, 6) graphical rendering properties, 7) soundproperties and 8) bonus properties. The properties for the 3-D objectspecified in the initial state may be used to generate the 3-D gameobject's trajectory in the gaming environment and the game outcomepresentation associated with the 3-D game object.

The trajectory of the 3-D game object may be viewed as comprising asequence of trajectory states with an initial state, a final state andone or more states between the initial state and the final state. Thetrajectory states describe the 3-D game object's path through the 3-Dgaming environment including its position and velocity as a function oftime. The trajectory of the game object in a 3-D gaming environmentincluding the various trajectory states may be formatted for a gameoutcome presentation on the gaming machine.

A format used to present the trajectory to the game player is important.In some formats, the trajectory of the game object in the 3-D gamingenvironment may not be of particular interest to a game player. Forexample, the trajectory of the game object may be represented as list ofnumbers indicating the position and velocity of the game object as afunction of time. Displaying these numbers on a display screen on thegaming machine would likely not be of particular interest to most gameplayers. Thus, the trajectory of the game object in the gamingenvironment is converted into a format that provides entertainment tothe game player. The format is typically referred as a game outcomepresentation.

The game outcome presentation may comprise a sequence of presentationstates. The presentation states describe a presentation of thetrajectory states on a gaming machine interface. The presentation statesmay include but are not limited to images, visual effects, sound effectsand other effects that are designed to stimulate a player's senses whilethe player is playing the trajectory-based game of chance on the gamingmachine. Typically, the images from the presentation states allow theplayer to view the 3-D game object's progression along its trajectory inthe 3-D gaming environment. Details of presentation states and method ofgenerating the presentation states for a gaming machine interface thatmay be used with the present invention are described in co-pending U.S.application Ser. No. 10/041,212, by Breckner, et al. and titled,“Decoupling Of The Graphical Presentation of A Game From ThePresentation Logic” which is incorporated herein in its entirety and forall purposes.

As described above, when the 3-D game object is inserted into the 3-Dgaming environment, the initial state for the 3-D game object maydescribe a number of properties of the 3-D game object. The propertiesmay be used to generate the trajectory states of the object along itstrajectory and corresponding presentation states that are used in a gameoutcome presentation. The initial position, the initial velocity, massproperties, the geometry and physical properties may be used to generatea trajectory of the 3-D game object in the 3-D gaming environment 300.These properties may also be defined for the 3-D objects in the 3-Dgaming environment. The initial position and initial velocity of the 3-Dgame object in the initial state may be used as a set of initialconditions for generating the trajectory.

The mass properties may include but are not limited to a mass, a centerof gravity for the 3-D game object and moments of inertia. The geometryfor the 3-D game object may include a plurality of surfaces and/or datapoints that are used to describe the geometry of the 3-D game object.The physical properties may include but are not limited to a density, asurface elasticity of the object, and a drag coefficient. The physicalproperties that are specified may depend on the trajectory rules used tomodel the 3-D game object's motion (See FIG. 1B for more details). Forinstance, if the drag of the game object is modeled than an area and thedrag coefficient of the object may be needed. Otherwise, theseproperties may not be required.

To generate the trajectory of the 3-D game object, the initial position,initial velocity, mass properties, the geometry and the physicalproperties of the 3-D game object and the properties of other objects inthe 3-D gaming environment 300 may be used with a set of trajectoryrules and a set of collision rules. The trajectory rules are used todescribe the motion of the 3-D game object in the 3-D gamingenvironment. The trajectory rules may be a set of equations that arenumerically integrated in time to generate the trajectory of the 3-Dgame object. The collision rules are used to determine the effects ofcollisions between the 3-D game object and other objects in the 3-Dgaming environment along its trajectory. The collisions may result in achange in momentum for the 3-D game object and a corresponding change invelocity of the 3-D game object. The collision rules and trajectoryrules are described in more detail with respect to FIG. 1B.

The graphical rendering properties, sound properties and bonusproperties are used to generate the presentation states for the gameoutcome presentation of the trajectory-based game of chance. Typically,these properties are not used to simulate the 3-D game object'strajectory (e.g., position and velocity) in the gaming environment.However, these properties may be used to distinguish between differenttypes of objects. For instance, red objects may be assigned one set ofphysical properties while blue objects may be assigned a different setof physical properties. The player may be able to distinguish betweenobject's with different properties according to their color or someother graphical rendering property such as a texture or a shade.

The graphical rendering properties may describe, for example, a shadingand a color of the 3-D game object along its trajectory. The shading andthe color of the 3-D game object may be rendered into 2-D images used ina game outcome presentation that are derived from the 3-D gamingenvironment. Other graphical rendering properties are described in moredetail with respect to FIG. 8.

The sound properties may be used to determine sounds that are generatedwhen the 3-D game object collides with another object or surface in the3-D gaming environment 300. The sounds may be used in a presentationstate for the game outcome presentation of the trajectory-based game ofchance. The bonus properties may be used to describe bonus game eventsthat may be triggered when the 3-D game objects interacts with otherobjects along its trajectory. For example, in one embodiment of thepresent invention, a bonus game may be triggered when the 3-D gameobject collides with a particular object or surface along its trajectoryin the 3-D gaming environment. The bonus properties for the 3-D gameobject may be used to determine what type of bonus game is generated.Further details of bonus games are described with respect to FIG. 6.

To illustrate the generation of trajectory states, a few examples oftrajectories of 3-D game objects in the gaming environment are provided.The present invention is not limited to these examples. The examples arealso used to illustrate methods that may be used to add excitement tothe game outcome presentation for the trajectory based game of chance.The methods of adding excitement to the game outcome presentation mayinvolve changing the properties of the game object along its trajectory,changing the properties of other objects in the gaming environment andtriggering game events, such as bonus games. These methods are used toadd elements of unpredictability and variability to the trajectory-basedgame of chance that a game player may find entertaining.

In one embodiment of the present invention, the properties of the gameobject and the properties of objects in the gaming environment may bechanged and game events may be triggered in response to different eventsthat may occur along the trajectory of the game object. For example, thegame object's properties and the properties of other objects in thegaming environment may be changed in response to collisions between thegame object and other objects along its trajectory and to the gameobject passing through or entering a particular area in the gamingenvironment. Also, the properties of objects may be changed and gameevents may be triggered in response to the generation of a random numberand to satisfying one or more conditions that are tracked in thetrajectory-based game of chance. Bonus games and other aspects of thegame outcome presentation such as the generation of audio effects andvisual effects on the gaming machine may also be triggered by theseevents. Details of these effects in the context of three trajectoriesare described below.

For a first trajectory, a spherical game object 330 is inserted in the3-D gaming environment at location 342 with an initial state ofproperties. Next, the spherical game object passes through an opening331 in the planar surface 329. The spherical game object collides with afirst rectangular box 350, which is an object in the 3-D gamingenvironment. In response, to the collision, the 3-D game object istransformed into a diamond shaped object 332. The diamond shaped object332 then collides with a second rectangular box 351 and is transformedin to a pyramidal shaped game object 333. Then the game object leavesthe gaming environment 300 through the exit 334. In general, the gameobject may be polyhedron with a plurality faces. The sphere 330, thediamond 332 and the pyramid 333 are examples of polyhedra that may begenerated in the 3-D gaming environment 300 and used as game objects.Dice and coins (not shown) are other examples of polyhedra that may begenerated in the 3-D gaming environment.

Along the trajectory starting at 342, the geometry of the game object330 changes twice. The velocity of the game object changes direction,for instance, each time the game object bounces off the rectangularboxes, 350 and 351. Further, the magnitude of the velocity may changealong its trajectory. For example, the game object 330 may accelerate ordecelerate along its trajectory.

The physical and mass properties of the game object 330 may remainconstant along its trajectory. For example, the trajectory andcollisions for the game object 330 may be generated as though the gameobject 330 remains a sphere 330 with a specified elasticity and masseven after it changes shape to a diamond and then to a pyramid. Asanother example, the physical properties and mass properties of the gameobject may change along the trajectory. For instance, the elasticity ofthe game object 330 may be decreased or the mass of the object may beincreased after each collision. When the properties of the game objectare altered in this manner, the game object may rebound less and lessafter each collision.

The graphical rendering properties, sound properties and the bonusproperties of an object may change along its trajectory. For example,each time the game object 330 collides with an object, its color maychange. Thus, the game object 330 may start out red, turn green afterhitting the first rectangular box 350 and turn gold after hitting thebox 351. In a similar manner, the sound the game object 330 makes inresponse to a collision may also change along its trajectory. A firstsound may be generated when the game object 330 collides with the firstrectangular box 350 and a second sound may be generated when the gameobject collides with the second rectangular box 351.

Bonus properties for the game object may change along its trajectory. Inone embodiment, a bonus event may be triggered on the gaming machinethat is independent of the position and velocity of the game objectalong its trajectory. For instance, the bonus event may be triggered atrandom time intervals. At the initial state of 342, the game object 330may be assigned a bonus property which is a number of free game objectswhere each game object may be used to play a trajectory based game ofchance. As the game object 330 collides with different objects in thegaming environment 330, the bonus property, which is the number of freegame objects associated with the game object 330, may increase or maydecrease. When a bonus event is triggered during the game object'strajectory 330, the number of free game objects currently associatedwith the game object is awarded.

For example, the bonus property for the game object 330 may be 1 freegame object at the initial state at 342 and may increase to 4 free gameobjects after collision with the first box 350 and may decrease to zerogame objects after the collision with box 351. Therefore, along the gameobject's trajectory, when the bonus event is triggered at a time wherethe game object is between location 342 and the collision with box 350,one game object may be awarded. Between the collision with box 350 andthe collision with box 351, 4 game objects may be awarded if the bonusis triggered during this portion of the trajectory. Finally, after thecollision with box 351, no game objects may be awarded if the bonusevent is triggered during this portion of the trajectory.

In response to collisions, the properties of objects in the gamingenvironment 300, besides game objects, may change. For example, thefirst rectangular box may change color after it struck by the gameobject 330. As another example, the rectangular box 350 may change shapeafter a collision. For instance, the rectangular box 350 may appeardented after a collision with the game object 330. The dent may healitself after a while or may remain in the box 350. In general, any ofthe properties of the game object and the second object may change inresponse to a collision including but not limited to the geometryproperties, the mass properties, the physical properties, the graphicalrendering properties, the bonus properties and the sound properties.Also, all or a portion of the properties may remain constant after acollision. For example, the game object's shape or color may not changein response to a collision.

A collision between a game object and a second object in the gamingenvironment may induce motion in the second object. For instance, whenthe first rectangular box 350 is struck by the game object 330, it maybegin to translate, to rotate or to vibrate in response to thecollision. The box 350 may rotate in place or vibrate in place and thenstop after a while or it may begin to translate around the gamingenvironment. For example, the box 350 may vibrate as though it wereattached to an invisible string that ran through the center of the boxand was anchored on both ends.

In response to a collision between objects in the gaming environment300, other aspects of the trajectory based game of chance may bemodified besides the properties of the game objects. For example, in oneembodiment, a bonus game in the trajectory-based game of chance may betriggered when the collision is detected. In another embodiment, a gameevent may be triggered when the collision is detected. The game eventmay be used trigger one or more presentation events in a presentationstate of the trajectory-based game. For instance, as part of apresentation state, the game event may trigger an activation of a lightpanel located on the gaming machine, an activation of a bonus wheel onthe gaming machine, the projection of a particular sound throughspeakers on the gaming machine or the generation of a new object in thegaming environment 300 that is rendered in the game outcomepresentation.

A second trajectory for a spherical game object 322 is initiated atlocation 341. The spherical game object collides with a firstrectangular box and a second rectangular box and passes through an area321. In response to the intersection of the game object with the area321, one or more properties of the game object 322, such as but notlimited to a position, a velocity, a mass property, a geometry, physicalproperties, graphical rendering property, a sound property and a bonusproperty, may be modified. Also, in response to the intersection, theseproperties may be modified for other objects in the gaming environment.

As an example, in response to the intersection, the game object 322 maybe transported to another location in the gaming environment in adiscontinuous manner, such as being transported from the intersectionlocation in the area 321 to a location 325. In yet another example, inresponse to the intersection, the game object may be instantaneouslyaccelerated or decelerated. In general, one or more of the game object'stranslational, rotational and vibrational velocity components may bemodified. In yet another example, in response the intersection with thearea 321, the game object's shape or color may change. The area 321 maybe as small as a single coordinate in the gaming environment 300. Theoperations described above may also be triggered when the game objectmay also passes through a volume instead of an area, such as 321.

In other embodiments, in response to the intersection between the gameobject 322 and the area 321, one or more of the following may beimplemented: 1) the game object's trajectory may be terminated as partof an exit rule, 2) the game object may be removed from gamingenvironment as part of an exit rule, 3) a bonus game event may betriggered and 4) a game event may be triggered. For example, when thearea that is intersected by the game object is an exit to the gamingenvironment, then the game object's trajectory is terminated and thegame object is removed from gaming environment. In another example, whenthe area that is intersected by the game object is an entrance to abonus storage area, such as a cup, the game object's trajectory may beterminated and the game object may be temporarily stored in the storagearea. However, the game object is not removed from the gamingenvironment 300 and may later be reintroduced into the gamingenvironment in response to another game event. Details of bonus storageareas are further described with respect to FIG. 7.

After the game object 322 passes through the area 321, it bounces offthe surface 329 and enters the opening 323. After passing through theopening 323, the game object is transported to location 325 in adiscontinuous manner. This differs from the trajectory of the gameobject 330 that starts at location 342. In this trajectory, after thegame object 330 passes through the surface 329 through opening 331, thegame object's trajectory is continuous in that it is not altered when itpasses through the opening. From location 325, the game object 322collides off a rectangular box, bounces off a planar surface 352 andexits the gaming environment 300 through the exit 353.

A third trajectory for a spherical game object 320 is initiated atlocation 340. The game object 320 collides off a rectangular box 357 andsplits into three game objects. In the present invention, in response toa collision with an object in the gaming environment which may includeanother game object or in response to the object passing through anarea, such as area 321, the game object may be split into a plurality ofobjects. The split of the game object may be triggered by other eventssuch as at random or in response to other parameters tracked in thegaming environment. The game object's velocity magnitude or a distancedtraveled along its trajectory are two examples of parameters that may betracked in the gaming environment. In this example, the game object 320is split into three objects. Two of the objects are spherical shaped andone of the object is diamond shaped.

In one embodiment, the splitting of a first game object may result in anumber of new game objects. For instance, when game object 320 is splitinto three objects. The three new objects may be treated as separategame objects in the trajectory-based of game of chance where a distincttrajectory is generated for each of these new game objects. This type ofsplit may be implemented as part of a bonus game for thetrajectory-based game of chance. In another embodiment, the game objectmay split into a number of pieces to simulate an explosion. In thiscase, after the explosive split, the new pieces comprising the gameobject may be removed from the gaming environment.

In yet another embodiment, rather than splitting into new objects, inresponse to a collision with an object in the gaming environment, whichmay include another game object, or in response to the object passingthrough an area, such as area 321, new objects, which may be gameobjects, may be introduced into the gaming environment 321. For example,the rectangular box 357 may store the spherical object and the diamondshaped object. When the game object 320 collides with the rectangularbox 357, the spherical object and the diamond shaped object may bereleased from the box 327 along separate trajectories while the gameobject 320 continues along its trajectory. The diamond shaped object andthe spherical object released from the box 327 may become new objects inthe gaming environment 300 or these objects may become new game objects.

In a further embodiment, in response to a collision with an object inthe gaming environment, in response to the object passing through anarea, such as area 321, or in response to another conditions, such as atregular intervals, a size of an object may change. For example, when thegame object 320 collides with rectangular box 357, the size of the gameobject 320 may increase/decrease and/or the size of the rectangular boxmay increase/decrease. In another example, a size of an opening, such as331 or 356, may increase or may decrease as a function of time.Therefore, when the opening is large compared to a size of a gameobject, the game object may pass through the opening. When the openingis small compared to the size of a game object, the game object maybounce off the opening.

In response to a collision between two objects in the gamingenvironment, the two objects, rather than splitting, may merge into oneanother. For example, the game 320 after colliding with the rectangularbox collides with a second rectangular box and embeds itself into asecond rectangular box 358. After the collision, the game object may bestored in the rectangular box 358 and later released in response to agame event or the game object may be removed the gaming environment 300.In another example, two game objects may collide with one another andthe two game objects, rather than bouncing off of one another or causingeach other to explode, may merge together to create a single gameobject. Further, objects in the gaming environment 300 other than gameobjects may collide and merge with another and then split apart again ata later time.

In another embodiment of the present invention, in response to acollision or in response to an object passing through an area, objects,surfaces or exits may appear in the gaming environment or disappear fromthe gaming environment 300 or the objects, surfaces, exits may bemodified in some manner. For instance, the opening 354 in the planarsurface 329 may lead to a bonus area. The opening 354 may not appearuntil a game object (or another object in the gaming environment)collides with a particular object in the gaming environment or passesthrough an area in the gaming environment. When the opening 354 has notappeared in the planar surface 329, the surface where the opening 354appears may behave as a solid surface and objects may collide off of it.When the opening 354 has appeared, then the game object may pass throughthe opening 354.

In general, one property that may change as a function of time in thegaming environment is the solidity of an object or a solidity of asurface. At one time, an object or surface in the gaming environment maybehave as a solid that prevents objects from passing through it and atanother time the object or the surface may act as a non-solid an allowobjects to pass through them. For instance, the solidity of a gameobject may be changed so that the game object passes through one or moreobjects in the gaming environment rather than colliding with the object.As another example, the solidity of a surface, such as the planarsurface 329, may change such that the game object 322 may bounce off itat one time and pass through it at another time. Further, surfaces maybe selectively permeable allowing certain objects to through them whilebeing impermeable to other objects.

In yet another embodiment, in response to an intersection or in responseto a collision, an object or a surface may be actuated in a manner thatopens or closes an opening in the gaming environment. For instance, inresponse to a collision or an intersection, a door blocking an exit mayopen, allowing an object to pass through it, or the door may closeblocking objects from passing through it. In another example, a surfacemay slide back and forth between two adjacent openings in response to acollision, an intersection or at random. Therefore, when the firstopening is blocked by the surface, the second opening is unblocked andwhen the second opening is blocked by the surface, the first opening isunblocked.

In a further embodiment, rather than an opening appearing or an openingdisappearing, in response to a collision or an intersection, an objectmay appear in the gaming environment or the object may disappear fromthe gaming environment. For example, in response to a collision, a domemay appear over an exit that blocks objects from passing through theexit. As another example, a wall blocking an entrance to a portion ofthe gaming environment may be removed allowing objects to pass throughthe entrance in response to different events that may occur in thegaming environment.

As described above, collisions or intersections between objects andsurfaces in the gaming environment 300 may be used to trigger variousgame events, such as the changing of one or more of a game object'sproperties. The surfaces or the objects involved in the collisions orintersections may be rendered as visible or invisible in the gamingenvironment. For example, the gaming environment 300 may be bounded byinvisible or translucent walls. The invisible walls may deflect objectsthat collide with them. As another example, objects or surfaces in thegaming environment 300 that can be used to generate collisions orintersections, such as the rectangular boxes, 357 and 351, and thesurface 321 may be rendered as invisible objects.

In general, the visibility characteristics of an object or a surface mayvary with time. For example, a surface, such as area 321 may remaininvisible until an object such as the game object 322 intersects thearea 321. At the time of the intersection between the game object 322and the area, the surface may become visible for a brief time and thenbecome invisible again after a period of time. In another example, thebox 351 may become visible and invisible at regular intervals.

As described above, collisions or intersections may be used to triggerdifferent changes in the trajectory-based game of chance. The changesmay also be triggered by other methods. In one method, a change in oneof the aspects of the gaming environment, such as an object'sproperties, may be triggered at random. In another method, the change inone of the aspect of the gaming environment may be triggered based upona time interval. For instance, a game object's shape may change atregular intervals in the gaming environment independent of anycollisions or intersections by the game object. In yet another method,the change in one of the aspects of the gaming environment may betriggered after a sequence of conditions has occurred. For example, anopening in the gaming environment may not appear until a number ofspecific collisions and/or intersections has occurred between gameobjects and other objects in the gaming environment. In one embodiment,one of the conditions in a sequence of conditions may be based upon awager made in the trajectory-based game of chance, such as an amount ofthe wager.

The generation of a trajectory of a game object in a 3-D gamingenvironment is only part of the generation of trajectory-based game ofchance that is presented on a gaming machine. As described above, aspart of a presentation state for the trajectory-based game of chance,which may include a plurality of effects that are designed to stimulateone or more the game player's senses, a sequence of 2-D images may berendered from the 3-D gaming environment. The sequence of game imagesmay be rendered using one or more virtual cameras in the 3-D gamingenvironment.

For the purposes of illustration, two virtual cameras, 302 and 306 areshown in the FIG. 1A. The first virtual camera is located at a locationin front and above of the planar surface 329. The virtual camera is usedto “capture” a portion of the 3-D gaming environment and to render theportion of the 3-D gaming environment to a 2-D image. The space in the3-D environment captured by the first virtual camera 302 is representedby the dashed lines connected to the camera. A 2-D image of the spacecaptured from the first virtual camera is shown in 312. The 2-D image312 may be included in a sequence of 2-D images used as part of the gameoutcome presentation for the trajectory based game of chance.

The position of the virtual camera 302 does not capture any portion ofthe trajectories of the game objects in the gaming environment. Thevirtual camera may be positioned to capture all or a portion of one moreof game object's trajectory in the 3-D gaming environment. The positionof the virtual camera used in a trajectory-based game of chance may varyfrom one trajectory-based game of chance to another trajectory-basedgame of chance and does not have to remain fixed. The position of thevirtual camera may also vary during the trajectory-based game of chance.Further, a plurality of virtual cameras may be used to generate thesequence of 2-D images used to generate the game outcome presentationfor the trajectory-based game of chance. For instance, a game outcomepresentation for a trajectory-based of chance may use images renderedfrom cameras 302 and 306. In one embodiment of the present invention,the gaming machine may be designed to allow the game player to select alocation of a virtual camera.

The second virtual camera, 306, is located on the game object 322. Aspace captured by the virtual camera is defined by the dashed linesconnected to the camera. The camera captures a rectangle 308 of theplanar surface 352. The space captured by the camera 310 is renderedinto a 2-D image 310. The virtual camera 322 may travel with the gameobject 322. For instance, as the game object 322 travels toward thesurface 352, the 2-D images rendered from the camera may show thesurface 352 appearing to get closer and closer. Additional details ofusing the virtual camera are described with respect to FIG. 8 and aswell as co-pending U.S. application Ser. No. 09/927,901, filed Aug. 9,2001, by LeMay, et al., and titled, “Virtual Cameras And 3-D GamingEnvironments In A Gaming Machine,” previously incorporated herein.

Three trajectories, starting at locations 340, 341, and 342,respectively in the gaming environment 300, have been described. Thesetrajectories are a function of a number of variables such as the initialstate of the trajectory, properties of the game object and the placementof objects in the gaming environment. In general, all of the possibletrajectories for game objects in the gaming environment 300 are not usedin a trajectory-based game of chance. Theoretically, for each gamingenvironment with its individual placement of objects and exits, thenumber of possible trajectories is infinite. However, various criteriarelated to the application of the trajectory-based game of chance to agaming machine are available that provide some guidelines in regards totrajectory selection.

One criterion on a gaming machine that effects the trajectory selectionis a length of time for a game outcome presentation for a game ofchance. The length of time of a game outcome is usually on the order ofa few seconds. Thus, the trajectory selection may be limited to a groupof trajectories that are within a range of times bounded by a minimumtime and a maximum time. For example, trajectories may be selected thatlast between 1 and 3 seconds.

Another criterion for trajectory selection is that game player'sgenerally prefer rules and outcomes for the game of chance which areeasy to understand. For example, in gaming environment 300, onlytrajectories that result in a game object leaving the gaming environment300 through one of the exits 334 or 353, 355, 356 within a bounded rangeof times may be used. When the game object leaves through one of theexits, the trajectory-based game of chance ends with a result that iseasy for a player to understand.

Yet another criterion for trajectory selection is variability of thetrajectories. Typically, when a game is monotonous without muchvariability, a game player may quickly lose interest in playing thegame. Thus, a group of trajectories and a gaming environment may beselected that provides for trajectories with a large degree ofvariation.

An illustration of how the criteria listed above may be satisfied isprovided by comparing the trajectory-based games of chance of thepresent invention to two mechanical systems used in gaming that involvethe trajectory of a moving object: 1) roulette and pachinko. The gamingenvironment 300, including trajectory rules, collision rules, exit rulesand the properties of objects, may be modeled after a mechanical system,such as roulette or pachinko. However, as discussed in detail below, thepresent invention is not constrained to the physical and the mechanicallimitations of these mechanical systems.

In a mechanical roulette game, a roulette wheel with a number of slotsis surrounded by a bowl-like surface. To play the game, the roulettewheel is spun and a ball is inserted into the bowl-like surface with aninitial velocity. The ball travels around the bowl-like surface until itlands in one of the slots of the spinning roulette wheel. After the balllands in one of the slots, it may bounce from slot to slot until itcomes to rest in a final slot. The final slot the ball comes to rest indetermines the outcome of the roulette game. The path of ball around thebowl-like surface including collisions and bounces in the slotscomprises its trajectory.

In the 3-D gaming environment, the bowl-like surface, the spinning wheeland the trajectory of the ball around the bowl and bounces in the slotsmay be simulated as part of the generation of a trajectory-based game ofchance. In the 3-D gaming environment for roulette, the trajectory ofthe game object may include simulating a game object moving along thebowl-like surface while in a medium, such as air, and moving through theair without contact with a surface. In general, in the 3-D gamingenvironments of the present invention, objects may be simulated movingthrough different media, such as water, oil or air, while in contactwith a surface in the gaming environment or moving through the mediawithout contact to a surface in the gaming environment.

Pachinko is another example of a mechanical system that may be modeledas a trajectory-based game of the present invention. A single game ofmechanical pachinko involves dropping a ball through a portion of avertical box. The ball starts at the top of the box and is drawn throughthe box via the force of gravity. A large number of obstacles may bearranged within the box. As the ball falls through the box, thetrajectory of the ball is altered by collisions with the obstacles. Thethickness of the box is usually not much greater than the diameter ofthe ball. Therefore, the velocity component of the ball in the directionperpendicular to the face of the box is very small and the trajectory ofthe ball is substantially planar.

A number of exits are placed within the box that allow a ball to leavethe portion of the box where the collisions are taking place. A gameoutcome is determined by the exit from which the ball leaves the box.The game is designed such that the trajectory of the ball is verysensitive to its initial conditions. Thus, it is very difficult topredict the trajectory of the ball within the box and hence the exitfrom which the ball leaves. Further, the game is designed such that theball always leaves through one of the exits independent of the initialconditions of the trajectory.

The obstacles, the exits, the effects of collisions of the balls withobstacles, the falling of balls in response to gravity and otherqualities of a mechanical pachinko game may be simulated in the 3-Dgaming environment of the present invention. Similar to a mechanicalpachinko game, the trajectories of the ball may be limited to planartrajectories in the 3-D gaming environment. Also, like a mechanicalpachinko system, the 3-D gaming environment may be designed such thatobjects always leave the gaming environment through one of a pluralityof exits. Further, devices, such as flippers used to impart momentum toa game object or plungers used to launch a game object (see FIG. 9) mayalso be simulated in the 3-D gaming environment.

The trajectory-based games of the present invention have many advantagesover mechanical systems such as the roulette game and the pachinko gamedescribed above. A few of these advantages are described as follows.First, the properties of trajectory-based games of the present inventiondo not change in an unpredictable manner over time. The properties ofmechanical systems may change over time due to wear. Second, thetrajectory-based games of the present invention are not limited byactual physics. For example, in the pachinko game or the roulette, theobjects always fall according to the earth's gravity. In a 3-D gamingenvironment of the present invention, the gravity on the moon, Jupiter,Mars or even anti-gravity may be modeled to create differenttrajectories. Further, in the mechanical roulette game and the pachinkogame, the force of gravity is essential constant throughout the system.In a 3-D gaming environment, the physical forces modeled in the systemsuch as the force of gravity may be substantially varied throughout thegaming environment.

In the present invention (see FIG. 6 for more details), a 3-D gamingenvironment for trajectory-based game of chance may be modeled where agame object travels through many different media, such as air, water andoil. In the mechanical roulette and pachinko systems, the ball movesthrough air. Although it would be possible to use different substancesin a mechanical pachinko game, such as water, it is not practical formaintenance reasons. In the present invention, game objects of manydifferent shapes may be employed, such as spheres, boxes, pyramids anddiamonds. In a mechanical trajectory game, such as pachinko, sphericalballs are used because they are easy to gather and circulate in amechanical system. Using non-spherical objects such as boxes or pyramidswould be impractical because of the difficulty of mechanically gatheringand circulating non-spherical objects. Further, in a mechanical system,changing the shape of the game object, such as from a sphere to adiamond, or splitting the game object into a number of pieces is notfeasible.

In the mechanical roulette and pachinko games, the mechanical systemsare designed such that the ball always ends up in an exit independent ofthe initial velocity and position of the ball in the system. Themechanical games are designed this way so that precise control of theinitial state of the game object, such as its position and velocity, isnot needed. In the present invention, the initial state of the gameobject is easily specified. Thus, trajectory-base games of chance in 3-Dgaming environments may be implemented where the final state of the gameobject is dependent on both the design of the gaming environment (e.g.,object placement and exit rules) and the initial state of the gameobject.

As an example, a trajectory-based game of chance may be implemented in a3-D gaming environment where the game objects enter the gamingenvironment at a specific location and are required to exit through oneof a plurality of exits in the gaming environment. The gamingenvironment may be designed such that only game objects that enter thegaming environment at the specific location with a sub-set of possibleinitial velocities leave the gaming environment through one of theplurality of exits. Initial velocities outside of the subset may resultin the game object not leaving the gaming environment, which would notbe desirable. Thus, unlike mechanical pachinko or mechanical roulette, agame object entering the gaming environment at the specific location maynot end up at an exit independent of its initial velocity. However, inthe present invention, since the initial velocity of the game object maybe precisely specified, the game objects may be given initial velocitiesthat always lead to trajectories where the game object leaves the gamingenvironment through one of the plurality of exits. Initial velocitieswhere the game objects do not leave the gaming environment through anexit are not used. The generation of initial conditions for game objectsin a trajectory-based game of chance is described in more detail withrespect to FIG. 3.

Yet another advantage of the 3-D gaming environments of the presentinvention as compared to mechanical system is the capability ofcontrolling of the view used in the game outcome presentation. In amechanical system such as the roulette game or the pachinko game, theorientation of the mechanical system does not change and a single viewor a limited range of views is provided to the player. For instance, inmechanical pachinko game, the system is designed to remain verticallyoriented and the view from in front of the pachinko game of the ballsfalling through the vertical surface is the only view presented to theplayer. As described above, a virtual camera in the 3-D gamingenvironment may be used to render a sequence of 2-D images used in thegame outcome presentation for the trajectory-based game of chance. Theposition of the virtual camera may be moved throughout the 3-D gamingenvironment and the position may change as a function of time. Forinstance, as described, the virtual camera may be located on the gameobject. Thus, a view from the perspective of the game object may begenerated. With mechanical systems, such a pachinko, variable views frommany different perspectives are not feasible.

FIG. 1B is a block diagram describing trajectory rules and collisionrules for two objects, 370 and 371, in the 3-D gaming environmentdescribed with respect to FIG. 1A. The two diamond shaped objects 370and 371 may be two game objects, a game object and an object in the 3-Dgaming environment, or two objects in the gaming environment. Asdescribed above, the game object is distinguished from other moving orstationary objects in the 3-D gaming environment in that a wager is madeon an aspect of the game object's trajectory in the trajectory-basedgame of chance. The trajectories of objects in the gaming environmentbesides game objects may be simulated but wagers are not made on theirtrajectories. The trajectory rules and collision rules used to generatethe trajectories of game objects and non-game objects may be the same ormay be different.

Using well-known physical relations, a realistic appearing trajectoryfor an object in a 3-D gaming environment including collisions may begenerated. The purpose of using the physical relations may be togenerate a realistic presentation of a game object moving and collidingwith various objects in the gaming environment. However, the presentinvention is not limited to using physical relations that occur innature. For instance, as described above, the effects of anti-gravitymay be modeled in the 3-D gaming environment. In general, the accuracyof the simulations is not important as long as it is appealing to aplayer playing the trajectory-based game of chance.

In FIG. 1B, the trajectory rules and the collision rules for twoobjects, 370 and 371, are described. The first object, 370, is allowedto translate in three directions and rotate in three directions in the3-D gaming environment. The second object 371 is allowed only totranslate in 3 directions in the 3-D gaming environment. For the firstobject 370 and the second object 371, the trajectory rules used togenerate a position and translation velocity of the game object as afunction of time may be specified as three equations of motion in the x,y and z directions relative to the object's centers of mass. For thefirst object, three additional equations of motion are used to determinerotational velocity components in a particular direction. For thetranslation velocity components, the velocity in a particular directionas function time is determined by integrating the equation, F=mA where Fis the summation of translational forces in a particular direction, m isthe mass of the object and A is the acceleration in the particulardirection. This equation may be integrated a second time to determinethe position of the center of mass of the objects as a function of timein a particular direction in the gaming environment.

In a similar manner, the rotational forces for the first object 370 maybe modeled as Fr-I.theta. where Fr is a summation of rotational forceabout a particular axis, I is a moment of inertia about the particularaxis and .theta. is an angular acceleration. Assuming no rotationalcoupling, 3 equations may be written to account for the rotationalforces around each axis. To generate a rotational velocity and arotational position as a function of time, each force equation may beintegrated twice. More complex equations (up to nine equations toaccount for all of the cross coupling terms in 3-D dimensions) may beused to simulate rotational coupling in the gaming environment but thislevel of complexity is unlikely to be needed in a game presentation on agaming machine. Although not shown, vibrational force equations may bewritten to simulate the vibrational motion of an object about its centerof mass as a function of time.

Each of translation force in the summation of forces in each forceequation may be a function of a number of parameters such as but notlimited to: i) a position (x,y,z) in the gaming environment, ii) thetranslation velocity of the game object (Vx,Vy,Vz), iii) rotationalvelocities (Rx, Ry, Rz), iv) time, v) vibrational velocities (notshown), vi) various physical constants of the object and the environment(not shown), such as a gravitational constant, mass properties of theobject, a drag constant for the object, etc. Similarly, other forcesmodeled in the gaming environment, such as rotational forces andvibrational forces, may also be a function of these parameters.Gravitational forces, frictional forces, inertial forces, environmentalforces, electromechanical forces, electromagnetic forces and imaginaryforces may be modeled in the gaming environment and incorporated in oneor more force equations. However, the present invention is not limitedto these forces.

Frictional forces may include the drag on an object as it moves througha substance such as air or water in the gaming environment or thefriction between the object and a surface in the gaming environment.Inertial forces may include centrifugal forces. Electromechanical forcesmay include the forces from electromechanical devices simulated in thegaming environment such as springs or flippers that may come in contactwith objects in the gaming environment. These forces may be also bemodeled as part collision rules describing the effects of collisionsinvolving the object. Electromagnetic forces imparted by a magneticfield or the magnetic properties of objects may be simulated in thegaming environment. Environmental forces may include the effects of windin air environment or water currents in a water environment. Imaginaryforces may include the effects of forces not found in nature such asanti-gravity or a frictional force that speeds up an object ratherslowing it down.

As an example, to simulate the diamond shaped object falling throughwater in the gaming environment, mass properties of the diamond shapedobject (e.g., a density, a volume, a mass distribution, etc.), a dragcoefficient of the object and constants used to model viscous drag inthe water may be specified. Then, force equations used to model theforces in one or more directions may be generated. The force equationsmay include the effects of gravitational forces, buoyancy forces,viscous forces and environmental forces (e.g., water currents in thegaming environment). With an initial velocity and an initial position inthe gaming environment for the object, the trajectory, includingvelocity and position as a function of time of the game object startingfrom the initial velocity and the initial position, may be generated byintegrating the one or more force equations.

In this example, when the effects of rotation are modeled for theobject, then rotational force equations accounting for the effects ofviscous drag on the object may also be generated. With an initialrotation velocity, the rotational velocity of the object in the gamingenvironment may be determined along its trajectory by integrating therotational force equations. As described above, the trajectory as afunction of time of the game object in the gaming environment may beused as part of a game outcome presentation on the gaming machine.

As described above, to generate a trajectory, one or more forceequations may be integrated. For complex force equations, a numericalintegration technique may be applied to solve the force equations. Insome embodiments, a closed form solution may be available for theintegrated force equations and numerical integration may not berequired. In this case, the force equations may be integrated togenerate a formula where the formula provides the trajectory of theobject as a function of time.

As described with respect to FIG. 1A, a game object may collide withvarious objects along its trajectory. Also, non-game objects may alsocollide in the gaming environment. When two objects collide in thegaming environment, the velocity of one or both of the objects may bechanged. The velocities of the objects may include translational,rotational and vibrational velocity components. For collisions betweentwo objects in the gaming environment, such as but not limited to a gameobject and a non-game object, collision rules may be specified that areused to determine the effects of a collision on one or more of thevelocity components of each object.

The collision rules may or may not be physics-based. For example, onecollision rule, which is not physics-based, may be that red coloredobjects are not affected by collisions. A collision rule that isphysics-based may account for the change in momentum of the two objectsduring a collision. For instance, a physics-based collision rule thatmay be used to described a linear, elastic collision between the twogame objects, 370 and 371, at collision location 372 is based upon thephysical conservation of momentum during the collision. Given theinitial translational velocities and masses of the two objects prior tothe collision, equations may be derived that provide the finalvelocities of the two objects after the collisions. In FIG. 1B, anequation that provides the final velocity of each object, V1.sub.f andV2.sub.f based upon the mass of each object, m.sub.1 and m.sub.2, andthe initial velocity of each object V1.sub.i and V2i is shown. Morecomplex equations may be derived that account for the effects ofnon-linear collisions and non-elastic collisions. In additions,equations may be derived that describe changes in rotational andvibrational velocities that may result from a collision between twoobjects.

In one embodiment, the collision rules may account for forces applied toan object during a collision. For example, an object along itstrajectory may collide with a spring loaded platform where the springloaded platform imparts a force to object that effects itspost-collision velocity of the object. In another example, the gamingenvironment may include flippers that impart a velocity to an objectwhen the flipper and the object collides.

FIG. 2 is a flow chart depicting a method 900 of generating a trajectoryfor a game object in a 3-D gaming environment of the present invention.2-D images rendered from the gaming environment showing the game objectalong its trajectory may be used as part of a game outcome presentationfor a trajectory-based game of chance. The method may also be applied togenerate a trajectory for a non-game object in the 3-D gamingenvironment. However, a wager is not associated with the trajectory ofthe non-game object.

In the method, a trajectory comprising a sequence of states may begenerated for a game object. The sequence of states may include aninitial state, a final state and one or more states between the initialstate and the final state. For each state, information regardingproperties in the gaming environment, such as but not limited to 1) aposition, 2) a velocity which may include a translational velocity, arotational velocity, a vibrational velocity and combinations thereof, 3)mass properties, 4) a geometry, 5) physical properties, 6) graphicalrendering properties, 7) sound properties and 8) bonus properties, maybe either specified or generated.

To generate a second state in the sequence of states from a first state,the properties of the game object at first state may be modified byapplying game logic, such as but not limited to trajectory rules andcollision rules. The game logic relates the properties of the firststate to the properties of the second state. By repeatedly applying thegame logic to generate new states, the sequence of states of the gameobject along its trajectory are generated. As an example, typically, forthe initial state, the properties of the game object are specified. Theinitial position and the initial velocity of the game object may bespecified by selecting the initial position and the initial velocityfrom a database of positions and velocities (see FIG. 3 for moredetails). The database may also include a geometry, physical propertiesand graphical rendering properties that are used to specify theseproperties for the game object. Then, to generate a second state afterthe initial state, the properties specified for the initial state may bemodified according to the game logic. To generate a third state afterthe second state, the game logic may be applied to the properties of thegame object at the second state. The process may be repeated until afinal state in the sequence of states is generated.

Typically, in the sequence of states only information from one state isused to generate the next state in the sequence of states. For instance,the third state is generated from the second state or the N.sup.th stateis generate N.sup.th−1 state. This method is described in FIG. 2.However, the present invention is not so limited. Information from aplurality of states may be used to generate a state in the sequence ofstates. For example, the third state in the sequence of states may begenerated from information from a second state and information a firststate.

In 905, the properties of the game object in the gaming environment atthe first state are looked up. The first state refers to one of thestates in the sequence states for the game object along its trajectorythat is used to generate the immediately following state in the sequenceof states. It is not limited to the initial state in the sequence ofstates. In 910, information used to apply the trajectory rules is lookedup. The trajectory rules may vary from location to location in thegaming environment. Thus, the information may specify a set oftrajectory rules to apply. After the trajectory rules to apply aredetermined, the physical properties need to apply the trajectory rulesmay be looked up. The physical properties used in the gamingenvironment, such as a gravitational constant, may vary from location tolocation. Therefore, the local physical properties at the first statemay be determined. When the trajectory rules and the physical propertiesare constant throughout the gaming environment, 910 may be eliminated.In 915, the trajectory rules are applied to generate an initial set ofproperties at the second state.

In 920, it is determined whether the game object has collided with anyobjects between the first state and the second state. In 925, when acollision has been detected, the properties of the colliding objects maybe looked up. Also, the collision rules to apply in the collision mayalso be determined. In 930, the collision location may be generated. Thecollision location is the location where the two objects make contactwith one another. The collision location may depend on the geometry ofthe two objects in the collision. After the collision location isgenerated, the location of the center of mass of the game object in thegaming environment may be generated. Typically, the position of thecenter of mass of the game object in the gaming environment is generatedfor its trajectory. Thus, when the two objects are in contact, thelocation of the center of mass of the game object at this point maybecome the position of the game object for the second state.

In 935, the collision rules may be applied to generate the postcollision velocity of the game object and other changes to the gameobject's properties. The collision rules were described with respect toFIG. 1B. As described with respect to FIG. 1A, properties of the gameobject such as its graphical rendering properties, sound properties andbonus properties may be changed as a result of a collision. Thecollision rules may specify the conditions for which changes to theproperties are made.

In 940, events triggered by the collision may be processed. In FIG. 1A,a number of game events that may occur in response to a collision aredescribed. In 940, it is determined whether any game events haveoccurred and any game events that have occurred are processed. Forinstance, in response to a collision, one or more of the following mayoccur: 1) the game object may be transported to another location, 2) thegame object may be split into a plurality of game objects, 3) gameobjects may be released into the gaming environment, 4) the game objectmay explode and 5) a bonus game may be triggered. Additional examplesare described in FIG. 1A. A game event that is triggered from thecollision may change the game object's properties at the second statesuch as when the game object is transported to another location inresponse to a collision.

In 945, it determined whether the game object as intersected an areathat is used to trigger a game event. After it is determined that anarea that may trigger a game event has been intersected, in 950, it isdetermined whether any game events have been triggered. Then, in 950,any game events that have been triggered are processed. For example, inresponse to an intersection, one or more of the following may occur: 1)the game object may be transported to another location, 2) the gameobject may be split into a plurality of game objects, 3) game objectsmay be released into the gaming environment, 4) the game object mayexplode and 5) a bonus game may be triggered. Additional examples aredescribed in FIG. 1A. A game event that is triggered from theintersection may change the game object's properties at the second statesuch as when the game object is transported to another location inresponse to a collision.

In 955, after the second state of the game object has been determined,one or more exit rules may be applied to the game object. The exit rulesdetermine when the game object's trajectory is terminated and the gameobject is removed from the game. Details of exit rules are describedwith respect to FIG. 1A. In 960, it is determined whether the trajectoryof the game object has been terminated. In 965, when the game objecttrajectory is terminated, the game object may be removed from the gamingenvironment and an outcome for the trajectory-based game of chance maybe displayed. The outcome may indicate an award for the trajectory-basedgame of chance.

In 967, it is determined whether any game events have been triggeredbased upon a parameter tracked along the trajectory. Then, any triggeredgame events may be processed. For example, as was described with respectto FIG. 1A, a game event may be triggered in response to a distancetraveled along the trajectory, a time along the trajectory, a number ofcollisions along the trajectory or based-upon a combination ofconditions. The game events that may be triggered are the same that maybe triggered in response to a collision or an intersection with an area.

In 970, the position and velocity of the game object and otherproperties of the second game state may be stored. In 975, the gameobject may be rendered according to the properties of the second statein the gaming environment. Next, the properties of the second state maybecome the properties of the second state looked up in 905 an the methodmay be repeated until the trajectory of the game object is terminated in960.

FIG. 3 is a flow chart depicting a method of generating a pay-table fora trajectory-based game of chance. In 600, for a 3-D gaming environment,objects are generated. The objects may include all of the differentshapes and surfaces in the 3-D gaming environment and their geometry's.In 602, the interaction rules for the 3-D gaming environment aregenerated. The interaction rules may comprise game logic and parametersused to describe the behavior of objects in the gaming environment, suchas how the objects interact in response to different conditions.

The interaction rules may include but are not limited to: 1) trajectoryrules and their associated parameters, 2) collision rules and theirassociated parameters, 3) exit rules and their associated parameters and4) any additional logic and parameters needed to specify game eventsthat are triggered by the interaction of objects in the gamingenvironment. As an example, as described with respect to FIG. 1B, thecollision rules may comprise: 1) equations used to model momentumexchange between two objects during a collision and 2) logical rulesthat are used to determine how other properties of an object, such as acolor, a shape or a size, are changed in response to the collision. Touse the momentum exchange collision rules, an elasticity parameter maybe assigned to each object and/or surface in the gaming environment. Ingeneral, each object in the gaming environment may be assigned manydifferent parameters that are used in logical rules implemented in thegaming environment.

In 604, after the 3-D gaming environment and the associated logic usedto describe the behavior of objects in the gaming environment has beenspecified, an insertion point for inserting game objects into the gamingenvironment may be selected. The insertion point is a location in thegaming environment where the trajectory of a game object is initialized.One or more insertion points may be used in a trajectory-based game ofchance. In FIG. 1A, three trajectories with three different insertionpoints in the gaming environment 300 are described.

In 606, the properties of the game object are initialized at theinsertion point. The game object may be initialized with a randomvelocity within a specified range of velocities. In 608, a trajectoryfor the game object in the gaming environment is generated. Thetrajectory may comprise a sequence of states with an initial state, afinal state and plurality of states in between the initial state and thefinal state where property information is specified at each state.

In 610, the trajectory may be compared to one or more criteria used todetermine whether the trajectory is acceptable for storage to atrajectory database. For example, a length of a time between the initialstate of the trajectory and the final state of the trajectory may begenerated and compared to an acceptable range of times where onlytrajectories within the range of times are accepted. In another example,a number of collisions along the trajectory may be generated andcompared to an acceptable range of collisions where only trajectorieswithin the range of collisions are accepted. Many criterions arepossible and are not limited to these examples.

In 612, when a trajectory is accepted, the trajectory may be stored to atrajectory database. In the trajectory database, information describingthe trajectory may be stored. For instance, the properties of the gameobject at its initial state and one or more states along its trajectory,such as the final state, may be stored to the trajectory database. Inaddition, information about aspects of the trajectory that may be usedfor a wager in a trajectory-based game of chance may be stored in thetrajectory database. For example, an exit location of the trajectory, anumber of collisions along the trajectory, a length of distance of thetrajectory, a length of time of the trajectory, a final velocity of thetrajectory or a maximum velocity along the trajectory are aspects of thetrajectory that may be used for a wager that are stored in thetrajectory database.

In 614, after the trajectory has been accepted or rejected, additionaltrajectories may be generated at the insertion point in 606. Millions oftrajectories may be generated at each insertion point and stored in thetrajectory database. In 616, when all of the trajectories at a firstinsertion point have been generated, the process of generating aplurality of trajectories and storing the acceptable trajectories to thetrajectory database may be repeated at a second insertion point.

In 618, a set of game outcomes for trajectory-based game of chance maybe selected where a trajectory aspect is selected for each of the gameoutcomes in the set of game outcomes. For example, the set of gameoutcomes may include: 1) an award for trajectories where the gameobjects collides 5 or more times with an object, 2) an award fortrajectories where the game object collides with a particular object, 3)an award for trajectories where the game object leaves the game objectthrough a first exit in the gaming environment, 4) an award fortrajectories where the game object leaves the gaming environment througha second exit and 5) no award for any other trajectories. In 620, apaytable may be constructed where a probability of occurrence isassigned to each of the game outcomes in the set of game outcomes. Anaward for each game outcome may be proportional to the probability ofoccurrence for each game outcome.

In 622, the trajectory database may be used to map a plurality oftrajectories to each game outcome in the set of game outcomes. Atrajectory mapped to each game outcome is selected to satisfy thetrajectory aspect assigned to the game outcome. For example, when thegame outcome is based-upon a trajectory where the game object collides 5times or more times along its trajectory, then trajectory database maybe searched for trajectories where the game object collides 5 or moretimes along its trajectory. When a trajectory satisfying the searchcriteria is found, information that allows the trajectory to begenerated in the gaming environment, such as an initial position and aninitial velocity, may be stored to a trajectory table.

All of the information needed to generate the trajectory in the gamingenvironment may not be stored in the trajectory table. A trajectoryrecord in the trajectory in the trajectory table may point to othermemory locations, such as the trajectory database, that store additionalinformation needed to generate the trajectory. The number oftrajectories from the trajectory database that are mapped to each gameoutcome may vary from 1 to a large number. When a desired amount oftrajectories are not available, additional trajectories may begenerated.

In 624, the paytable and trajectory table may be installed on a gamingmachine. Then, a trajectory-based game of chance may be generated usingthe paytable and the trajectory table. For example, using the paytable,a game outcome defined in the paytable may be selected at random. Oncethe game outcome is selected, a trajectory corresponding to the gameoutcome may be selected from the trajectory table. The informationstored in the trajectory table and/or other memory locations may be usedto generate the trajectory in the gaming environment. When a pluralityof trajectories are available for the game outcome, one of the availabletrajectories may be selected at random. In one embodiment, the selectionof the trajectory may be influenced by one or more input parameters froman input device on the gaming machine (see FIG. 9 for more details).

In one embodiment of the present invention, the number of trajectoriesmapped to each game outcome in the trajectory table may be proportionalto the probability of each game outcome occurring. For example, when theprobability of a particular game outcome occurring is 10%, then 10% ofthe trajectories, out of a total amount of trajectories mapped to all ofthe game outcomes, may be mapped to the particular game outcome.Therefore, for a game outcome with 10% probability of occurring, if thetotal amount of trajectories that are mapped to the different gameoutcomes is 1,000,000, then 100,000 would be mapped to the game outcome.In this embodiment, the pay table may not be needed. Instead,trajectories may be randomly selected from the trajectory table.

FIG. 4 is a flow chart depicting a first method of generating atrajectory-based game of chance on a gaming machine using a 3-D gamingenvironment as described with respect to FIGS. 1A, 1B and 2. In 700, arequest is received to initiate a trajectory-based game of chance on thegaming machine. Prior to receiving the request to initiate the game awager may be made on the trajectory-based game of chance. The request toinitiate the trajectory-based game of chance may be received from a userinterface on the gaming machine (see FIG. 8 for more details).

In 705, using a pay table, a game outcome may be determined for thetrajectory-based game of chance. The game outcome may be a function ofthe wager amount. In 710, as was described with respect to FIG. 3, atrajectory may be selected from a trajectory table that corresponds tothe game outcome determined in 705. In 715, the selected trajectory maybe generated in the gaming environment. The trajectory may comprise asequence of states for a 3-D game object in a 3-D gaming environment. In720, a game outcome presentation may be generated for thetrajectory-based game of chance. The game outcome presentation mayinclude a sequence of 2-D images rendered from the 3-D gamingenvironment that are displayed on the display screen of a gamingmachine. One or more of the 2-D images in the sequence of 2-D images mayshow the 3-D game object in different states along its trajectory in the3-D gaming environment. In 725, at a conclusion of the game outcomepresentation, the game outcome for the trajectory-based game of chance,such an award amount, may be displayed to the display screen. Typically,the conclusion of the game outcome presentation includes the finalposition of the game object in the 3-D gaming environment.

In present invention, a plurality of trajectory-based games of chancemay be played in a serial manner or a parallel manner. In a serialmanner of game play of the plurality of trajectory-based games ofchance, after a wager is made on a first trajectory-based game ofchance, the method of generating the trajectory-based game of chancecomprising 700, 705, 710, 715, 720 and 725 is implemented. A secondtrajectory-based game of chance may not be initiated until the gameoutcome for the first trajectory-based game of chance has been displayedin 725. Then, method may be implemented for the second trajectory-basedgame of chance.

In a parallel manner of game play of the plurality of trajectory-basedgames of chance, after a wager is made on a first trajectory-based gameof chance, the method of generating the trajectory-based game of chancecomprising 700, 705, 710, 715, 720 and 725 is implemented. After thefirst game of chance has been initiated in 700, a wager may be made on asecond game of chance prior to the completion of the first game ofchance in 725. Then, the method, comprising 700, 705, 710, 715, 720 and725 may be implemented for the second game of chance. Therefore, theimplementation of the method for the first game of chance and the secondgame of chance may overlap. When the initiation of each trajectory-basedgame of chance is under player control, depending on when the playerinitiates each trajectory-based game of chance and length of time foreach trajectory-based game of chance in a sequence of trajectory-basedgames of chance played by the player, the trajectory-based games ofchance may be played in a serial manner, a parallel manner andcombinations thereof.

In one embodiment, only a trajectory of one game object may be simulatedin a gaming environment at a time. Therefore, when two trajectory-basedgames of chance are played in parallel, a trajectory for a first gameobject may be simulated in a first gaming environment and a trajectoryfor a second game object may be simulated in a second gaming environmentat the same time on the gaming machine. 2-D images rendered from thefirst gaming environment and 2-D images rendered from the second gamingenvironment may be displayed to a single display screen on a gamingmachine using a split screen display format. The first gamingenvironment and the second gaming environment used in the trajectorysimulations may be the same (e.g., same format and same logical rules)or the two gaming environments may differ (e.g., different format and/ordifferent logical rules). In the present invention, one or more 3-Dgaming environments may be stored on the gaming machine and used for thepurposes of generating a trajectory for a game object used in atrajectory-based of chance.

In another embodiment, the trajectories for a plurality of game objectsmay be simulated in a single gaming environment at the same time.Therefore, when two trajectory-based games of chance are played inparallel, a trajectory for a first game object and a second game objectmay be simulated in the gaming environment at the same time on thegaming machine. 2-D images rendered from the gaming environment anddisplayed to a display screen on the gaming machine may includetrajectory states from both objects in the same 2-D image. Details ofparallel game playing methods that may be used with the presentinvention are described in co-pending U.S. application Ser. No.09/553,437, filed on Apr. 19, 2000, by Brosnan et al, entitled “ParallelGames on a Gaming Machine,” which is incorporated herein by reference inits entirety and for all purposes.

FIG. 5 is a flow chart depicting a second method of generating atrajectory-based game of chance on a gaming machine. In the presentinvention, a gaming environment may be designed where it is difficult todetermine the outcome of a trajectory, a priori and outcome of thetrajectory simulation may not be known until the simulation is completedin the gaming environment. A gaming environment where the properties ofthe gaming environment change as a function of time is example of agaming environment that may be difficult to determine the outcome oftrajectory, a priori.

In a gaming environment that changes as a function of time, the objectsin the environment may move around, different objects may appear or maydisappear, and the interaction rules, such as trajectory rules andcollision rules, may be time varying. Thus, the trajectory of the gameobject may depend on both its initial state and a state of the gamingenvironment when the game object is inserted into the gamingenvironment. For instance, two game objects may be introduced into thegaming environment with the same initial state at different times. Whena state variation for the gaming environment is the same following theintroduction of the game objects, the game objects travel along the sametrajectory. However, when the state variation for the gaming environmentis different following the introduction of the game objects, the gameobjects may travel different trajectories even though their initialstates are the same.

When the properties of the gaming environment change as a function oftime, it may not be desirable to develop a trajectory table for eachstate of the gaming environment. Instead, in one embodiment, the gamingenvironment may be designed and initial states for game objects in thegaming environment may be selected such that on average over time a setof game outcomes for a trajectory-based game of chance with a certainset of probability distributions is achieved. The set of game outcomesmay be based-upon different aspects of a game object's trajectory, suchas its final position in the gaming environment. In this embodiment, thegame outcome may not be determined until the game object reaches itsfinal state in its trajectory in the gaming environment.

The average probability distribution for the set of game outcomes may beverified by performing a Monte Carlo simulation where the trajectoriesof a large number of game objects with different initial states and atdifferent environment states are analyzed. In this embodiment, it isimportant to determine whether the probabilities of a game outcome varyin time according to changes in the gaming environment. If a game playercan alter their probability of winning the trajectory-based game ofchance by timing when they play the game, then the game may beconsidered a game of skill, which may not be desirable in somejurisdictions. Therefore, in most cases, the gaming environment may bedesigned to avoid the possibility of the game player being able to gainan advantage based upon their skill in playing the game.

In 800, a request is received to initiate a trajectory-based game ofchance on the gaming machine. Prior to receiving the request to initiatethe game a wager may be made on the trajectory-based game of chance. Therequest to initiate the trajectory-based game of chance may be receivedfrom a user interface on the gaming machine (see FIG. 8 for moredetails). In 805, an initial state for a game object in the gamingenvironment is selected. In 810, the selected trajectory may begenerated in the gaming environment. The trajectory may comprise asequence of states for a 3-D game object in a 3-D gaming environment. In815, a game outcome presentation may be generated for thetrajectory-based game of chance. The game outcome presentation mayinclude a sequence of 2-D images rendered from the 3-D gamingenvironment that are displayed on the display screen of a gamingmachine. One or more of the 2-D images in the sequence of 2-D images mayshow the 3-D game object in different states along its trajectory in the3-D gaming environment.

In 820, the game object is removed from the gaming environment and thegame outcome for the trajectory-based game of chance is determined. Thegame outcome may be based upon one or more aspects of the game object'strajectory such as but not limited to its final position in the gamingenvironment, a number of collisions, etc. In 825, at a conclusion of thegame outcome presentation, the game outcome for the trajectory-basedgame of chance, such an award amount, may be displayed to the displayscreen.

In one embodiment, to eliminate the possibility of the game outcomebeing influenced by a player's skill, an element of randomness may beintroduced to the gaming environment. For example, the gamingenvironment may be designed such that the game object is constrained toleave the gaming environment through one or more exits. Different awardsmay flash randomly over the exits. The game outcome may be the awardthat is showing when the object enters the exit. The random variation ofthe awards may prevent a player from using skill to influence the gameoutcome.

FIG. 6 is a block diagram of a 3-D gaming environment where propertiesof the 3-D gaming environment vary as a function of space and time. Atrajectory-based game of chance may be played using trajectories of gameobjects simulated in the 3-D gaming environment. In one embodiment, theblock diagram 400 may be a 2-D image rendered from a planar 3-D gamingenvironment. The 2-D image may be displayed on the display screen of agaming machine.

A trajectory for a game object, such as 410, is initialized at aninitial state in the gaming environment at the entrance 412. The gamingenvironment is designed with five exits, 408 and 415, 416, 417 and 418,and the game object is constrained such that it exits the gamingenvironment through one of the five exits. The game outcomes for thetrajectory-based game of chance are based-upon which exit the gameobject leaves the gaming environment. When the game object leaves thegaming environment through one of the four exits 415, 416, 417 and 418,an award for the trajectory-based game of chance is generated. When thegame object leaves the gaming environment through the exit 408, thewager on the trajectory-based game of chance is lost.

The gaming environment 400 is divided into four regions, 401, 402, 404and 406. Region 401 is a rectangular region that surrounds exit 415.Region 402 is a circular region above exit 416. Region 404 is an ovalshaped region that surrounds exit 408. Region 406 is the remainingregion outside of regions 401, 402 and 404 in the gaming environment.

The interaction rules, such as trajectory rules, collision rules andexit rules may vary from one region to another region. Further, theinteraction rules may vary in each region as a function of time. Forexample, a gravitational force may be modeled as part of the trajectoryrules in region 406 where the gravitational force causes the game objectto fall from the top of the gaming environment 419 to the bottom of thegaming environment 420. The bottom of the gaming environment is slopedsuch that game objects that reach the bottom 420 roll along the bottomuntil reaching exit 408. In region 401, a gravitational force may bemodeled as part of the trajectory rules where the game object falls inthe direction away from the bottom and towards the top 419 of the gamingenvironment 400.

Because gravity acts in the opposite direction between region 406 andregion 401, the entrance to exit 415 is orientated in opposite mannerfrom exits 416, 417, 418. Exit 415 is orientated so that a game objectcan fall up and into it. The entrance to the exits, 415, 416, 417 and418 are marked in FIG. 6. The sides of the exits, 415, 416, 417, and418, other than the entrance side, act as solid surfaces in regards to acollision with a game object. Exits 416, 417 and 418 are orientated sothat a game object may fall down into the exits through their entrances.

An example of a trajectory for the game object 410 that travels throughthe two regions 401 and 406 is shown in the FIG. 6. The game object 410enters the gaming environment through the entrance 412 with an initialforward velocity. The simulated gravitation forces in region 406 pullsthe object downward and it collides with an object in the gamingenvironment. Then, the game object 410 enters region 401 and begins tofall toward the top of the gaming environment 419 because gravity actsin the opposite direction in region 401 relative to region 406. The gameobject leaves region 401 and enters region 406 again where it is againaccelerated toward the bottom of the gaming environment 420. The gameobject 410 enters region 401 again where its velocity toward the bottomof the gaming environment is slowed before leaving region 401. The gameobject 410 then collides with two objects before colliding with thebottom 420 of the gaming environment. The game object 410 then bouncestwice off of the bottom and exits the gaming environment through exit408.

The trajectory rules for a region may be designed to draw an object intoa region or repel an object from the region. For instance, in region402, the trajectory rules may use an extremely large gravitationalconstant to simulate a force of gravity. The resultant gravitationalforce may be so large that any object that enters the region is alwaysdrawn into the entrance of the exit 416.

In similar manner, a gravitational force may be modeled to repelobjects. For example, in region 404 around exit 408, the trajectoryrules may include a gravitational force repels objects away from theexit. Normally, the gravitational force may be turned off so that gameobjects are allowed to enter the exit 408. However, when certainconditions are met in the trajectory-based of game of chance, therepelling gravitational force is activated such the game object is flungout of the region 404 before it enters the exit 408. The game objectflung out of the region may then enter one of the other exits, such as415, 416 or 418. Since the wager for the trajectory-based game of chanceis lost when the game object enters the exit 408, the repellinggravitational force may be activated as part of a bonus scenario for thetrajectory-based game of chance.

FIG. 7 is a block diagram used to describe bonusing and progressivescenarios for a 3-D trajectory-based game of chance. The gamingenvironment 400 is similar to the gaming environment described withrespect to FIG. 6 except that a bonus cup 424, a progressive cup 422 anda bonus board 426 have been added to the gaming environment.

A bonus property may be assigned to each game object at its initialstate, such as when it enters the gaming environment through entrance412. The bonus property may indicate a credit amount or a number of freegame objects that may be awarded when a bonus involving the game objectis triggered. In particular embodiments, the bonus credit amount or thebonus free game objects may be used for promotional purposes in thatthey may only be used for game play on the gaming machine but may not beredeemed for cash. As described with respect to FIG. 1A, the bonusproperty may change along the game object's trajectory such as inresponse to a collision with particular objects along the trajectory. Inthe present invention, it is not required to assign a bonus property toa game object. When a bonus is triggered involving a game object, abonus award may be generated at random.

In one embodiment, a bonus may be triggered when two game objectscollide. As described with respect to FIG. 4, a plurality oftrajectory-based games of chance may be played in parallel. In oneembodiment of parallel game play, the trajectories of a plurality ofgame objects may be simulated at the same time in the gamingenvironment. As an example, two trajectory-based games of chance may beinitiated with game objects 425 and 426. The two trajectory-based gamesof chance may be initiated separately and at different times. Forinstance, a first wager may be made and the trajectory-based game ofchance for game object 426 may be initiated and then a second wager maybe made and the trajectory-based game of chance for game object 425 maybe initiated. In the example, the trajectory for the game object 426 islonger than the trajectory for the game object 425 and the two gameobjects end up colliding. When the two game objects collide, the twogame objects explode and a bonus of “win 5” is awarded.

An advantage of awarding a bonus when two objects collide is that it mayencourage parallel game play. Parallel game play typically will resultin a higher game throughput, i.e. games player per unit time, thanserial game play. With a high game throughput, the casino may seeincreased revenues. Also, the high game throughput may allow the casinoto lower the game denomination amount, which may be desirable to somegame players.

In other embodiment, a bonus may be triggered when a game objectcollides with an object in the gaming environment or a group of objects.For instance, a bonus may be triggered when a game object collides withone of the bomb shaped objects 428. When the game object collides withthe bomb, the bomb and/or the game object may explode and the bonus istriggered. In another example, the bonus may not be triggered until eachof the bombs is exploded after a collision with a game object. Toexplode all of the bombs, a series of trajectory-based games of chancemay have to be played.

In general, a bonus may be triggered from a series of events that mayoccur over one or more trajectory-based games of chance. For instance, asymbol may be displayed on each of the exits to the gaming environment408, 415, 416, 417, 418. Each time an object leaves the gamingenvironment through one of the exits, the symbol on the exit may bedisplayed to the bonus board 426. When a particular combination ofsymbols is displayed, a bonus may be triggered. Otherwise, the bonusboard 426 may be reset.

In one embodiment, when a bonus is triggered, a large number of gameobjects may be released from the bonus cup 424. Awards may be earned foreach of the game objects released from the bonus cup 424 and additionalbonuses may be triggered. In one example, the bonus cup may start outempty and may be gradually filled by game objects that land in the bonuscup 424. When each game object lands in the bonus cup 424, a replacementgame object, i.e., a “free” game object, may be warded. When the bonuscup 424 becomes full, all of the game objects in the cup may bereleased. In another example, the cup 424 may start full. When a certainevent or a combination of events occur in the gaming environment, suchas a combination of symbols appearing on the bonus board 426, then thegame objects in the bonus cup may be released.

Different progressive awards may be incorporated into a trajectory-basedgame of chance. The progressive awards may be funded from a portion ofwagers from a plurality of trajectory-based games of chance. Thetrajectory-based games of chance used to fund the progressive awards maybe played by a single player or groups of players. Further, thetrajectory-based games of chance used to fund the progressive awards maybe played on different groups of gaming machines. The gaming machinesmay be connected via a casino area network or a wide area progressivenetwork. In another embodiment, the player may use a smart card, a cellphone or a personal computing device to play the progressive game. Aprogressive award may be awarded when a game object enters theprogressive cup 422.

FIG. 8 is a perspective drawing of a 3-D gaming environment implementedon a gaming machine for one embodiment of this invention. To utilize avirtual 3-D gaming environment for a game presentation or other gamingactivities on a gaming machine, a 2-D view of the virtual 3-D gamingenvironment is rendered. The 2-D view captures some portion of thesurfaces modeled in the virtual 3-D gaming environment. The capturedsurfaces define a 3-D object in the 3-D gaming environment. The capturedsurfaces in 2-D view are defined in the 3-dimensional coordinates of thevirtual 3-D gaming environment and converted to a 2-dimensionalcoordinate system during the capturing process.

In the present invention, the 2-D view is generated from a viewpointwithin the virtual 3-D gaming environment. The viewpoint is a mainfactor in determining what surfaces of the 3-D gaming environmentdefining a 3-D object are captured in the 2-D view. Since informationabout the 3-D gaming environment is stored on the gaming machine, theviewpoint may be altered to generate new 2-D views of objects within the3-D gaming environment. For instance, in one frame, a 2-D view of anobject modeled in the 3-D gaming environment, such as a front side of abuilding (e.g. the viewpoint captures the front side of a building), maybe generated using a first viewpoint. In another frame, a 2-D view ofthe same object may be generated from another viewpoint (e.g. thebackside of the building).

A disadvantage of current gaming machines is that the 2-D views used asvideo frames in game presentations are only rendered from 2-D objectsand information about the multi-dimensional nature of the objectsrendered in the 2-D views, such as the viewpoint used to generate the2-D view, are not stored on the gaming machine. Historically, due to theregulatory environment of the gaming industry, gaming software used topresent a game of chance has been designed to “run in place” on an EPROMinstalled on the gaming machine. Using an EPROM, it was not feasible tostore large amounts of game data. To generate and store pre-rendered 2-Dframes for a trajectory-based game of chance for every possibletrajectory would take a tremendous amount of memory. Using a 3-D gamingenvironment of the present invention and rendering 2-D frames for thetrajectories in real-time saves memory and allows for more trajectoriesto be used in the game design.

Returning to FIG. 8, the 3-D gaming environment 100 includes threeobjects: 1) a rectangular box 101 on top of, 2) a plane 114 and 3) asecond box 126. The box 101, box 127 and plane 114 are defined in a3-dimensional rectangular coordinate space 104. Typically, surfaces ofthe objects in the gaming environment are defined using a plurality ofsurface elements. The surface elements may comprise different shapes,such as different types of polygons that are well known in the 3-Dgraphical arts. For example, the objects in the present information maybe defined in a manner to be compatible with one or more graphicsstandards such as Open Graphics Library (OpenGL).

In one embodiment, the objects in the gaming environment 100 may bedefined by a plurality of triangular elements. As an example, aplurality of triangular surface elements 125 are used to define aportion of the surface 108 and the surface face 112. In anotherembodiment, the objects in the gaming environment 100, such as box 101and box 126, may be defined by a plurality of rectangular elements. Inyet another embodiment, a combination of different types of polygons,such as triangles and rectangles may be used to describe the differentobjects in the gaming environment 100. By using an appropriate number ofsurface elements, such as triangular elements, objects may be made tolook round, spherical, tubular or embody any number of combinations ofcurved surfaces.

Triangles are by the most popular polygon used to define 3-D objectsbecause hey are the easiest to deal with. In order to represent a solidobject, a polygon of at least three sides is required (e.g. triangle).However, OpenGL supports Quads, points, lines, triangle strips and quadstrips and polygons with any number of points. In addition, 3-D modelscan be represented by a variety of 3-D curves such as NURBs and BezierPatches.

Each of the surface elements comprising the 3-D virtual gamingenvironment may be described in a rectangular coordinate system oranother appropriate coordinate system, such as spherical coordinates orpolar coordinates, as dictated by the application. The 3-D virtualgaming environments of the present invention are not limited to theshapes and elements shown in FIG. 1 (see FIGS. 2, 3 and 4) or thecoordinate system used in FIG. 1 which are shown for illustrativepurposes only. Details of 3-D graphical rendering methods that may beused with the present invention are described in “OpenGL ReferenceManual: The Official Reference Document to Open GL, Version 1.2,”3.sup.rd edition, by Dave Shreiner (editor), OpenGL Architecture ReviewBoard, Addison-Wesley Publishing, Co., 1999, ISBN: 0201657651 and“OpenGL Program Guide: The Official Guide to Learning OpenGL, Version1.2,” 3.sup.rd edition, by Mason Woo, Jackie Neider, Tom Davis, DaveShreiner, OpenGL Architecture Review Board, Addison-Wesley Publishing,Co., 1999, ISBN: 0201604582, which are incorporated herein in theirentirety and for all purposes.

Surface textures may be applied to each of the surface elements, such aselements 125, defining the surfaces in the virtual gaming environment100. The surface textures may allow the 3-D gaming environment to appearmore “real” when it is viewed on a display screen on the gaming machine.As an example, colors, textures and reflectance's may be applied to eachof the surface elements defining the various objects in the 3-D gamingenvironment. Millions of different colors may be used to add a realistic“feel” to a given gaming environment. Textures that may be appliedinclude smoothness or surface irregularities such as bumps, craters,lines, bump maps, light maps, reflectance maps and refractance maps orother patterns that may be rendered on each element. The textures may beapplied as mathematical models stored as “texture maps” on the gamingmachine.

In one embodiment, the “texture map” may be an animated texture. Forinstance, frames of a movie or another animation may be projected onto a3-D object in the 3-D gaming environment. These animated textures may becaptured in 2-D views presented in video frames on the gaming machine.Multiple animated textures may be used at the same time. Thus, forexample, a first movie may be projected onto a first surface in the 3-Dgaming environment and a second movie may be projected onto a secondsurface in the 3-D gaming environment where both movies may be viewedsimultaneously.

Material properties of a 3-D surface may describe how the surface reactsto light. These surface properties may include such things as a) amaterial's ability to absorb different wave-lengths of light, b) amaterial's ability to reflect different wavelengths of light(reflectance), c) a material's ability to emit certain wavelengths oflight such as the tail lights on a car and d) a material's ability totransmit certain wavelengths of light. As an example, reflectance refersto how much light each element reflects. Depending on the reflectance ofa surface element other items in the gaming environment may be reflectedfuzzily, sharply or not at all. Combinations of color, texture andreflectance may be used to impart an illusion of a particular quality toan object, such as hard, soft, warm or cold.

Some shading methods that are commonly used with 3-D graphics to addtexture that may be applied to the present invention include gourandshading and phong shading. Gourand and phong shading are methods used tohide an object's limited geometry by interpolating between two surfaceswith different normals. Further, using Alpha Blending, pixels may beblended together to make an object appear transparent i.e. the objecttransmits light.

Virtual light sources, such as 102, may be used in the gamingenvironment to add the appearance of shading and shadows. Shading andshadows are used to add weight and solidity to the rendering of avirtual object. For example, to add solidity to the rectangular box 101,light rays emitted from light source 102 are used to generate a shadow103 around the rectangular box 101. In one method, ray tracing is usedto plot paths of imaginary light rays emitted from an imaginary lightsource such as 102. These light rays may impact and may reflect offvarious surfaces affecting the colors assigned to each surface element.In some gaming environments, multiple light sources may be used wherethe number of lights and the intensity of each light source change withtime. Typically, in real time 3D, the light sources do not generateshadows and it is up to the programmer to add shadows manually. Asstated earlier, however, the light sources produce shading on objects.

Perspective, which is used to convey the illusion of distance, may beapplied to the gaming environment 100 by defining a vanishing point,such as 126. Typically, a single point perspective is used where all ofthe objects in the scene are tendered to appear as though they willeventually converge at a single point in the distance, e.g. thevanishing point. However, multiple point perspectives may also beemployed in 3-D gaming environments of the present invention.Perspective allows objects in the gaming environment appear behind oneanother. For instance, box 101 and box 127 may be the same size.However, box 127 is made to appear smaller, and hence farther away, to aviewer because it is closer to the vanishing point 126. A 3-D gamingenvironment may or may not provide perspective correction. Perspectivecorrection is accomplished by transforming points towards the center ofthe 2-D view screen. The farther away an object is from the viewpoint in3-D gaming environment, the more it will be transformed into the centerof screen.

The present invention is not limited to perspective views or multipleperspective views of the 3-D gaming environment. An orthographic viewmay be used where 3-D objects rendered in a 2-D view always appear thesame size no matter how far away they are in the 3-D gaming environment.The orthographic view is what you would see as a shadow cast from alight source that is infinitely far away (so that the light rays areparallel), while the perspective view comes from a light source that arefinitely far away, so that the light rays are diverging. In the presentinvention, combinations of both perspective and orthographic views maybe used. For instance, an orthographic view of a text message may belayered on top of a perspective view of the 3-D gaming environment.

Related to perspective is “depth of field”. The depth of field describesan effect where objects that appear closer to a viewer are more in focusand objects that are farther away appear out of focus. Depth of fieldmay be applied renderings of the various objects in the gamingenvironment 100. Another effect that may be applied to renderings ofobjects in the gaming environment is “anti-aliasing”. Anti-aliasing isused to make lines which are digitally generated as a number of straightsegments appear more smooth when rendered on a display screen on thegaming machine. Because the 2D display only takes finite pixelpositions, stair stepping occurs on any limes that are not straight upand down, straight across (left and right) or at 45 degrees on thedisplay screen. Stair stepping produces a visually unappealing effect,thus, pixels are added to stair-stepped lines to make this effect lessdramatic.

Standard alpha-numeric text and symbols may be applied to one or moresurface elements in the gaming environment 101 to display gaminginformation to a game player. Other game features and gaming informationmay also be rendered in the gaming environment 100. For example, bonusgames, promotions, advertising and attraction graphics may also berendered in the gaming environment. For instance, a casino's logo or aplayer's face may be rendered in the gaming environment. Theseadditional game features may be integrated into a game outcomepresentation on the gaming machine or other operational modes of thegaming machine such as an attract mode.

After the gaming environment is defined in 3-dimensions, to display aportion of the 3-D gaming environment on a display screen on the gamingmachine, a “photograph” of a portion of the gaming environment isgenerated. The photograph is a 2-dimensional rendering of a portion ofthe 3-dimensional gaming environment. Transformations between 3-Dcoordinate systems and 2-D coordinate systems are well known in thegraphical arts. The photograph may be taken from a virtual “camera”positioned at a location inside the gaming environment 100. A sequenceof photographs taken by the virtual camera in the gaming environment maybe considered analogous to filming a movie.

A “photograph” displayed on the display screen of a gaming machine mayalso be a composite of many different photographs. For instance, acomposite photograph may be generated from portions of a firstphotograph generated using an orthographic view and portions of a secondphotograph generated using a perspective view. The portions of thephotographs comprising the composite photograph may be placed on top ofone another to provide “layered” effects, may be displayed in a “side byside” manner to produce a “collage” or combinations thereof.

Operating parameters of the virtual camera, such as its position at aparticular time, are used to define a 3-D surface in the gamingenvironment, which is projected on to a 2-D surface to produce thephotograph. The 3-D surface may comprise portions a number of 3-Dobjects in the 3-D gaming environment. The 3-D surface may also beconsidered a 3-D object. Thus, a photograph is a 2-D image derived from3-D coordinates of objects in the 3-D gaming environment. The virtualcamera may represent gaming logic stored on the gaming machine necessaryto render a portion of the 3-D gaming environment 100 to a 2-D imagedisplayed on the gaming machine. The photograph is converted into avideo frame, comprising a number of pixels, which may be viewed on adisplay screen on the gaming machine.

The transformation performed by the virtual camera allowing a portion ofthe virtual gaming environment to be viewed one or more display screenson the gaming machine may be a function of a number of variables. Thesize of lens in the virtual gaming environment, the position of thelens, a virtual distance between the lens and the photograph, the sizeof the photograph, the perspective and a depth variable assigned to eachobject are some of the variables that may be incorporated into atransformation by the virtual camera that renders a photograph of thevirtual gaming environment. The resolution of the display screen on thegaming machine may govern the size of a photograph in the virtualcamera. A typical display screen may allow a resolution of 800 by 600color pixels although higher or lower resolution screens may be used. A“lens size” on the virtual camera defines a window into the virtualgaming environment. The window is sometimes referred to as a viewport.The size and position of the lens determines what portion of the virtualgaming environment 100 the virtual camera views.

After the photograph of the virtual gaming environment has beengenerated, other effects, such as static and dynamic anti-aliasing, maybe applied to the photograph to generate a frame displayed on one ormore displays located on the gaming machine. Typically, the mathematicaland logical operations, which are encoded in gaming software logic,necessary to perform a particular transformation and generate a videoframe may be executed by video cards and graphics cards located on thegaming machine and specifically designed to perform these operations.The graphics cards usually include graphical processing units (GPUs).However, the transformation operations may also be performed by one ormore general purpose CPUs located on the gaming machine or combinationsof GPUs and CPUs.

In general, the 2D/3D video graphics accelerators or coprocessors, oftenreferred to as graphics processing units (GPUs), are located on orconnected to the master gaming controller and are used to performgraphical operations. The solutions described are most commonly found asvideo cards. The graphical electronics may be incorporated directly ontothe processor board (e.g. the master gaming controller) of the gamingmachine, and even tightly integrated within other very large scaleintegrated chip solutions. The integration methods are often cost savingmeasures commonly used to reduce the costs associated with massproduction. For instance, video cards, such as the Vivid!XS fromVideoLogic Systems (VideoLogic Systems is a division of ImaginationTechnologies Group plc, England) may used to perform the graphicaloperations described in the present invention. As another example, videocards from Nvidia Corporation (Santa Clara, Calif.) may be employed. Inone embodiment, the video card may be a multi-headed 3-D video card,such as a Matrox G450 (Matrox Graphics Inc., Dorval, Quebec, Canada).Multi-headed video cards let a single graphics card power two displayssimultaneously or render two images simultaneously on the same display.

When displaying photographs from a virtual camera in a 3-D gamingenvironment, a single image from the camera may be divided among aplurality of display devices. For instance, four display screens may beused to display one quarter of a single image. The video feeds for eachof the plurality of display devices may be provided from a single videocard. Multi-headed video cards let a single graphics card (or graphicssubsystem) display output on two or more displays simultaneously. Thismay be multiple output rendering for each display or one rendering overmultiple displays, or variation of both. For example, when amulti-headed video card is used, a first head on the multi-headed videocard may be used to render an image from a first virtual camera in a 3-Dgaming environment and a second head on the multi-head video card may beused to render a second image from a second virtual camera in a 3-Dgaming environment. The rendered first and second images from the firsthead and the second head may be displayed simultaneously on the samedisplay or the first image may be displayed on a first display and thesecond image may be displayed on a second display.

Returning to FIG. 8, three lenses, 105, 106 and 107 used in a virtualcamera are shown positioned at three locations in the virtual gamingenvironment. Each lens views a different portion of the gamingenvironment. The size and shape of the lens may vary which changes aportion of the virtual gaming environment captured by the lens. Forinstance, lenses 105 and 106 are rectangular shaped while lens 107 isoval shaped.

Lens 106 is positioned to view the “game display” for a game outcomepresentation rendered on surface 108. The portion of the gamingenvironment captured by lens 106 is a six-sided shape 120. As describedabove, the game display may contain the presentation of a particulargame played on the gaming machine, such as a hand of cards for a pokergame. After applying an appropriate transformation, a photograph 124 ofthe portion of the virtual gaming environment 100 in volume 120 isgenerated by the virtual camera with lens 106.

Using differing terminology common within the 3D graphics community, thelenses 105, 106 and 107 may be described as a camera. Each camera hasthe ability to have different settings. A scene in the 3-D gamingenvironment is shot from the camera's viewpoint. A different scene iscaptured from each camera. Thus, the scene is rendered from the camerato produce and image.

The photograph 124 generated from the virtual camera with lens 106 maybe viewed on one or more display screens on the gaming machine. Forinstance, photograph 124 may be viewed on a main display on the gamingmachine and a secondary display on the gaming machine. In anotherembodiment, a portion of photograph 124 may be displayed on the maindisplay and a portion of the photograph may be displayed simultaneouslyon a secondary display. In yet another embodiment, a portion ofphotograph 124 may be displayed on a first gaming machine while aportion of photograph 124 may be displayed simultaneously on a secondgaming machine.

Lens 105 of a virtual camera is positioned to view volume 121 in thevirtual gaming environment 100. The volume 121 intersects three faces,108, 110 and 112, of box 101. After applying an appropriatetransformation, a photograph 125 of the portion of the virtual gamingenvironment 101 in volume 121 is rendered by the virtual camera withlens 105 which may be displayed on one of the display screens on agaming machine.

Lens 107 of a virtual camera is positioned to view volume 122 in thevirtual gaming environment 100. The oval shape of the lens produces arounded volume 122 similar to a light from a flashlight. The volume 122intersects a portion of face 110 and a portion of plane 114 including aportion of the shadow 103. After applying an appropriate transformation,a photograph 126 of the portion of the virtual gaming environment 101 involume 122 is rendered by the virtual camera with lens 107 which may bedisplayed on one or more of the display screens on a gaming machine. Forinstance, a gaming machine may include a main display, a secondarydisplay, a display for a player tracking unit and a remote displayscreen in communication with the gaming machine via a network of sometype. Any of these display screens may display photographs rendered fromthe 3-D gaming environment.

A sequence of photographs generated from one or more virtual cameras inthe gaming environment 101 may be used to present a game outcomepresentation on the gaming machine or present other gaming machinefeatures. The sequence of photographs may appear akin to movie or filmwhen viewed by the player. For instance, a 3-D model of a virtual personmay appear to speak. Typically, a refresh rate for a display screen on agaming machine is on the order of 60 HZ or higher and new photographsfrom virtual cameras in the gaming environment may be generated as thegame is played to match the refresh rate.

The sequence of photographs from the one or more virtual cameras in thegaming environment may be generated from at least one virtual camerawith a position and lens angle that varies with time. For instance, lens106 may represent the position of a virtual camera at time, t.sub.1,lens 105 may represent the position of the virtual camera at time,t.sub.2, and lens 107 may represent the position of the virtual cameraat time t.sub.3. Photographs generated at these three positions by thevirtual camera may be incorporated into a sequence of photographsdisplayed on a display screen.

The position of the virtual camera may change continuously between thepositions at times t.sub.1, t.sub.2, t.sub.3 generating a sequence ofphotographs that appears to pan through the virtual gaming environment.Between the positions at times t.sub.1, t.sub.2, t.sub.3, the rate thevirtual camera is moved may be increased or decreased. Further, thevirtual camera may move non-continuously. For instance, a firstphotograph in a sequence of photographs displayed on a display screenmay be generated from the virtual camera using the position of lens 106.The next photograph in the sequence of photographs may be generated fromthe virtual camera using the position of lens 105. A third photograph inthe sequence of photographs may be generated from the virtual camerausing the position of lens 107. In general, the virtual camera in thegaming environment 101 may move continuously, non-continuously andcombinations thereof.

In a game presentation, a plurality of virtual cameras, with timevarying positions, in a plurality of virtual gaming environments may beused. The camera and environment information as a function of time maybe stored on the gaming machine and may be accessed when a particularscene for a game event in a game outcome presentation is needed suchthat the scene may be rendered in “real-time”. A scene may be defined bythe positions of one or more virtual cameras in one or more gamingenvironments as a function of time. The scenes may be modularized, i.e.a library of scenes may be generated, so that they may be incorporatedinto different games. For instance, a scene of a button being depressedmay be incorporated into any game using this type of sequence.

A sequence of photographs generated from a first virtual camera in afirst virtual gaming environment may be displayed simultaneously with asequence of photographs generated from a second virtual camera in asecond virtual gaming environment. For instance, the first sequence ofphotographs and second sequence and second sequence of photographs maybe displayed on a split screen or may be displayed on different screens.In addition, the first virtual camera in a first virtual gamingenvironment and the second virtual camera may be located in a secondvirtual gaming environment different from the first virtual gamingenvironment. Also, the first virtual gaming environment and the secondvirtual gaming environment may be in the same gaming environment.Further, a single virtual camera may jump between different gamingenvironments, such as between a game play environment to a bonus gamingenvironment. The transition between the gaming environments may alsoappear to be smooth (e.g. the camera may pan from one environment in acontinuous manner).

FIG. 9 is a block diagram depicting a user interface for a 3-Dtrajectory based game of chance. As described with respect to FIG. 1,the sequence of 2-D images rendered from the 3-D gaming environment maybe displayed to a display screen 34 on the gaming machine as part of apresentation state for the trajectory-based game of chance. A gameoutcome presentation for the trajectory-based game of chance, which maybe controlled by the master gaming controller 224 (See FIG. 11), maycomprise a sequence of presentation states.

In addition to the images displayed on the displayed screen, apresentation state may comprise outputs and inputs from various gamingdevices comprising the user interface 160 on the gaming machine that aredesigned to stimulate one or more of a player's senses including sight,sound, touch and smell. For example, sound effects, which may be outputfrom the sound projection devices 12 and 14, may provide auditorystimulation to the player. The plunger 110, the touch screen display 34and the control knob 118 may be used to provide inputs for thetrajectory-based game of chance and to provide tactile stimulation. Thelight panel 108 and the display 34 may be used to provide visualstimulation. In one embodiment, the display 34 may use a 16.times.9 or a9.times.16 aspect ration screen or any other type of non-square widescreen aspect ratio monitor screen. Additional gaming peripherals (notshown) connected to the user interface, such as bonus wheels andsecondary displays, may be used to provide further visual and auditoryeffects.

In one embodiment, the user interface 160 may include a plunger 110. Theplunger 110, like a pull handle on a mechanical or video slot game, maybe used to initiate the trajectory-based game of chance on the gamingmachine. The plunger 110 may be attached to a spring 112 that provide aresistive force when the plunger is pulled and returns the plunger to aninitial position when it is released. The plunger 110 may furthercomprise a strike pad 114 that is designed to strike an object, such asa ball 116, when the plunger is pulled back and released or when theplunger is pushed forward.

In another embodiment (not shown), a flipping mechanism comprising alever attached to a pivot may be used with the user interface 160. Whenthe lever on the flipping mechanism is pressed, the flipping mechanismmay impart a force to an object such as the ball 116. The force propelsthe object in a particular direction depending on how the object and thelever used in the flipping mechanism are aligned. Flipping mechanismsare common in mechanical pachinko games.

The user interface 160 may include a conduit 150, such as a hollow tube,that may be connected to the plunger 110 or the flipping mechanism. Theconduit 150 may be designed so that when the ball 116 is imparted with aforce, it travels up the conduit and then is returned to its initialposition 153 by the force of gravity. The force may be imparted to theball 116 by the plunger 110, the flipping mechanism or some othermechanism designed to impart a force to the ball. The conduit 150 may beconstructed from a translucent or clear material that allows the ball tobe viewed as it moves up the ball conduit 150.

In one embodiment, the top of the ball conduit 151 may be connected to asecond conduit 152 that returns the ball 116 to its initial position153. When the ball 116 is imparted with a force above a certainthreshold, the ball enters the second conduit 152 and it is returned toits initial position. When the ball 116 is imparted with a force below acertain threshold, it moves up the conduit 150 but does not reach thetop of the conduit 151 then rolls back down the conduit to its initialposition 153.

Mechanical gaming devices employed in the user interface 160 that may beoperated by a game player, such as the plunger 110, the ball conduit 150and the flipping mechanism, may include one or more sensors 102 that areused to measure an operational parameter of the device. For example,when the plunge is pulled back and released or pushed forward andreleased, the one or more sensors 102 may be used to measure that theplunger 110 has been moved and then returned to its initial position.The one or more sensors 102 may generate an output signal that is usedto indicate one of these events has occurred. When the master gamingcontroller 224 receives the one or more output signals from the sensors102, the master gaming controller may initiate a trajectory-based gameof chance.

One or more operational parameters measured by the sensors may be usedto influence one or more presentation states for the game outcomepresentation on the gaming machine. As an example of using informationmeasured from the sensors to influence the generation of a presentationstate, the distance the plunger 110 is pulled back may be determinedfrom the output signals generated by the sensors 102. Then, the distancemay be displayed on the user interface using an output device connectedto the interface. For instance, as the plunger 110 is pulled-back andreleased, the output signals from the sensors 102 may be used togenerate an animation on the display screen 34 where a video plunger 122is pulled back and released. As another example, this procedure could beduplicated for a flipping mechanism when a flipping mechanism is used inthe hardware interface.

As another example, the distance the plunger 110 is pulled back may be ameasure of how much force is imparted to the ball 116 when the plunger110 is released. Therefore, as the plunger 110 is pulled back, astrength meter on the display screen 120 and/or the light panel 108 maylight up. A number of lighted bars that are displayed on the strengthmeter 120 or A number of lights that are lit on the light panel 108 maybe proportional to the distance the plunger is pulled back. Further, asthe plunger is pulled back sounds may be emitted from the soundprojection devices. A pitch of the sound or some other characteristic ofthe sound may be selected according to the distance the plunger ispulled back.

In one embodiment, information measured from the sensors connected to amechanical input device may be used to select a trajectory for a gameobject in the trajectory-based game of chance. For example, the initialvelocity of the game object in the game environment may be selectedaccording to the distance the plunger 110 is pulled back before it isreleased. In another example, one or more sensors may be used a distancethe ball 116 travels along the conduit 150. The distance information maybe used as part of the selection of an initial trajectory for the gameobject in the trajectory-based game of chance.

As described with respect to FIG. 3, a large number of initial statesfor a game object including its initial velocity may generate the samegame outcome. Therefore, a game outcome may be determined at random andthen an initial state that corresponds to the game outcome may beselected from among the initial states that generate the desired gameoutcome. When a range of initial velocities, where some are higher andsome are lower, generate the same game outcome, then the distance theplunger is pulled back, as measured by the sensors, may be used toselect a trajectory with a higher initial velocity or a lower initialvelocity for use in the gaming environment.

When a trajectory is selected in this manner, it may appear to theplayer that they have some control over the game outcome because theycan control, to some degree, the type of game outcome presentation thatis generated by the master gaming controller. However, the generation ofthe game outcome is still generated at random by the master gamingcontroller 224 and is independent of the input by the player via theuser interface. Thus, the trajectory-based game may remain a game ofchance because the generated game outcome is not affected by the skillof player, such as how far they pull back the plunger 110.

The user interface may comprise additional input devices that may beused to affect a play of a trajectory-based game of chance. Thefollowing examples are provided for illustrative purposes only. Forexample, a shape control input 126 on the touch screen display 34 may beused to select a shape of the game object to use in the trajectory-basedgame of chance, such as a sphere, diamond or cube. In another example, adenomination control 128 may be used to select a default denominationfor game objects in the trajectory-based game of chance. The default isused unless a player specifies a wager in another manner for the gameobject. The strength meter may be used to provide input used to selectan initial state for the trajectory of the game object used in thetrajectory-based game of chance. For example, the strength meter 120 maybe used to select a higher or lower initial velocity for the game objectlike the plunger 110.

The control knob 118 may be used to select a game speed for thetrajectory-based game of chance. Turning the knob in one direction mayincrease the game speed. Turning the knob in another direction maydecrease the game speed. In one embodiment, a number of gametrajectory-based games of chance may be initiated automatically. Thecontrol knob 118 may be used to control the interval between theinitiation of successive games in the games that are initiatedautomatically.

Turning to FIG. 10, a video gaming machine 2 of the present invention isshown. Machine 2 includes a main cabinet 4, which generally surroundsthe machine interior (not shown) and is viewable by users. The maincabinet includes a main door 8 on the front of the machine, which opensto provide access to the interior of the machine. Typically, the maindoor 8 and/or any other portals which provide access to the interior ofthe machine utilize a locking mechanism of some sort as a securityfeature to limit access to the interior of the gaming machine. Attachedto the main door are player-input switches or buttons 32, a coinacceptor 28, and a bill validator 30, a coin tray 38, and a belly glass40. Viewable through the main door is a video display monitor 34 and aninformation panel 36. The display monitor 34 will typically be a cathoderay tube, high resolution flat-panel LCD, or other conventionalelectronically controlled video monitor. Further, the video displaymonitor 34 may be a touch screen. The touch screen may respond to inputsmade by a player touching certain portions of the screen. Theinformation panel 36 is a back-lit, silk screened glass panel withlettering to indicate general game information including, for example,the number of coins played. The bill validator 30, player-input switches32, video display monitor 34, and information panel are devices used toplay a game on the game machine 2. The devices are controlled by amaster gaming controller (not shown) housed inside the main cabinet 4 ofthe machine 2. Many possible games, including traditional slot games,video slot games, video poker, and keno, may be provided with gamingmachines of this invention.

The gaming machine 2 includes a top box 6, which sits on top of the maincabinet 4. The top box 6 houses a number of devices, which may be usedto add features to a game being played on the gaming machine 2,including speakers 10, 12, 14, a ticket printer 18 which printsbar-coded tickets 20, a key pad 22 for entering player trackinginformation, a florescent display 16 for displaying player trackinginformation, a card reader 24 for entering a magnetic striped cardcontaining player tracking information, and a video display screen 42.Further, the top box 6 may house different or additional devices thanshown in the FIG. 1. For example, the top box may contain a bonus wheelor a back-lit silk screened panel which may be used to add bonusfeatures to the game being played on the gaming machine. During a game,these devices are controlled, in part, by the master gaming controller(not shown) housed within the main cabinet 4 of the machine 2.

Understand that gaming machine 2 is but one example from a wide range ofgaming machine designs on which the present invention may beimplemented. For example, not all suitable gaming machines have topboxes or player tracking features. Further, some gaming machines haveonly a single game display—mechanical or video, while others aredesigned for bar tables and have displays that face upwards. As anotherexample, a game may be generated in on a host computer and may bedisplayed on a remote terminal or a remote gaming device. The remotegaming device may be connected to the host computer via a network ofsome type such as a local area network, a wide area network, an intranetor the Internet. The remote gaming device may be a portable gamingdevice such as but not limited to a cell phone, a personal digitalassistant, and a wireless game player. Images rendered from 3-D gamingenvironments may be displayed on portable gaming devices that are usedto play a game of chance. Further a gaming machine or server may includegaming logic for commanding a remote gaming device to render an imagefrom a virtual camera in a 3-D gaming environments stored on the remotegaming device and to display the rendered image on a display located onthe remote gaming device. Thus, those of skill in the art willunderstand that the present invention, as described below, can bedeployed on most any gaming machine now available or hereafterdeveloped.

Returning to the example of FIG. 10, when a user wishes to play thegaming machine 2, he or she inserts cash through the coin acceptor 28 orbill validator 30. At the start of the game, the player may enterplaying tracking information using the card reader 24, the keypad 22,and the florescent display 16. Further, other game preferences of theplayer playing the game may be read from a card inserted into the cardreader. During the game, the player views game information using thevideo display 34. Other game and prize information may also be displayedin the video display screen 42 located in the top box.

During the course of a game, a player may be required to make a numberof decisions, which affect the outcome of the game. For example, aplayer may vary his or her wager on a particular game, select a prizefor a particular game, or make game decisions which affect the outcomeof a particular game. The player may make these choices using theplayer-input switches 32, the video display screen 34 or using someother device which enables a player to input information into the gamingmachine. During certain game events, the gaming machine 2 may displayvisual and auditory effects that can be perceived by the player. Theseeffects add to the excitement of a game, which makes a player morelikely to continue playing. Auditory effects include various sounds thatare projected by the speakers 10, 12, 14. Visual effects includeflashing lights, strobing lights or other patterns displayed from lightson the gaming machine 2 or from lights behind the belly glass 40. Afterthe player has completed a game, the player may receive game tokens fromthe coin tray 38 or the ticket 20 from the printer 18, which may be usedfor further games or to redeem a prize. Further, the player may receivea ticket 20 for food, merchandise, or games from the printer 18.

FIG. 11 is a block diagram of networked gaming machines and gamingdevices that provide stand-alone trajectory-based game play, linkedtrajectory-based game play and progressive trajectory-based games forone embodiment of the present invention. A master gaming controller 224is used to present one or more games of chance on the gaming machines61, 62 and 63. The master gaming controller 224 may also act as atrajectory-based game controller. As a trajectory-based game controller,the master gaming controller 224 may be used to generatetrajectory-based games on one (e.g., stand-alone trajectory-based game)or more gaming machines (e.g., linked trajectory-based game). Forinstance, in linked trajectory-based game play, a plurality of gameplayers may play trajectory-based games of chance in a shared gamingenvironment. In one embodiment, the trajectory-based game may begenerated as a bonus game to the one or more games of chance played onthe gaming machines, such as 61, 62 and 63. Trajectory-based bonus gamemay be generated for a game of chance such as but not limited to videoslot games, video poker games, video black jack games, video card games,video keno games and mechanical slot games.

For a trajectory-based bonus game involving a plurality of linked gamingmachines, a trajectory-based game server 90 with a trajectory-based gamecontroller 92 may be used to generate the outcome of thetrajectory-based bonus game which is displayed on the plurality ofgaming machines such as 61, 62 and 63. The outcomes of thetrajectory-based bonus games and other linked trajectory-based games maybe based upon game play generated on the plurality of gaming machines incommunication with the trajectory-based game server 90. In oneembodiment, the trajectory-based game server may allow a game objectfrom a first gaming environment on a first gaming machine to travel to asecond gaming environment on a second gaming machine. In anotherembodiment, as described with respect to FIG. 2, the trajectory-basedgame server 90 or a gaming machine, such 61, 62 and 63, may provide aplurality of trajectory-based games in parallel i.e. at the same time.

The master gaming controller 224 executes a number of gaming softwaremodules to operate gaming devices 70, such as coin hoppers, billvalidators, coin acceptors, speakers, printers, lights, displays (e.g.34) and other input/output mechanisms (see FIG. 10). The master gamingcontroller 224 may also execute gaming software enabling communicationswith gaming devices located outside of the gaming machines 61, 62 and63, such as trajectory-based game servers (e.g., 90), trajectory-basedgame progressive servers (e.g., 82), player tracking servers, bonus gameservers, game servers, progressive game servers. In some embodiments,communications with devices located outside of the gaming machines maybe performed using the main communication board 215 and networkconnections 71. The network connections 71 may allow communications withremote gaming devices via a local area network, an intranet, theInternet or combinations thereof. The trajectory-based game server 90may also communicate with a number of game devices via the networkconnections 71 such as but not limited to the gaming machines 61, 62 and63, the trajectory-based game progressive server 82 and the remotegaming machines 64 and 65.

The gaming machines 61, 62 and 63 may use gaming software modules togenerate a trajectory-based game of chance that are distributed betweenlocal file storage devices and remote file storage devices. For example,to play a trajectory-based game on gaming machine 61, the master gamingcontroller may load gaming software modules into RAM 56 that may belocated in 1) a file storage device 226 on gaming machine 61, 2) antrajectory-based game server 90, 3) a file storage device 226 on gamingmachine 62, 4) a file storage device 226 on gaming machine 63, or 5)combinations thereof. In one embodiment of the present invention, thegaming operating system may allow files stored on the local file storagedevices and remote file storage devices to be used as part of a sharedfile system where the files on the remote file storage devices areremotely mounted to the local file system. The file storage devices maybe a hard-drive, CD-ROM, CD-DVD, static RAM, flash memory, EPROM's,compact flash, smart media, disk-on-chip, removable media (e.g. ZIPdrives with ZIP disks, floppies or combinations thereof. For bothsecurity and regulatory purposes, gaming software executed on the gamingmachines 61, 62 and 63 by the master gaming controllers 224 may beregularly verified by comparing software stored in RAM 56 for executionon the gaming machines with certified copies of the software stored onthe gaming machine (e.g. files may be stored on file storage device226), accessible to the gaming machine via a remote communicationconnection.

The trajectory-based game server 90 may also be a repository for gamesoftware modules and software for other game services provided on thegaming machines 61, 62 and 63. In one embodiment of the presentinvention, the gaming machines 61, 62 and 63 may download game softwaremodules from the trajectory-based game server 90 to a local file storagedevice to play a game of chance or an trajectory-based game. Thedownload of game software may be initiated by the trajectory-based gameserver 90. One example of a game server that may be used with thepresent invention is described in co-pending U.S. patent applicationSer. No. 09/042,192, filed on Jun. 16, 2000, entitled “Using a GamingMachine as a Server” which is incorporated herein in its entirety andfor all purposes. In another example, the game server might also be adedicated computer or a service running on a server with otherapplication programs.

In one embodiment of the present invention, the processors used togenerate a trajectory-based game may be distributed among differentmachines. For instance, the game flow logic to play an trajectory-basedgame may be executed on the trajectory-based game server 90 by thetrajectory-based game controller 92 while the game presentation logicfor the trajectory-based game may be executed on gaming machines 61, 62and 63 by the master gaming controllers 224. The gaming operatingsystems on gaming machines 61, 62 and 63 and the trajectory-based gameserver 90 may allow gaming events to be communicated between differentgaming software modules executing on different gaming machines viadefined APIs. Thus, a game flow software module executed on thetrajectory-based game server 90 may send gaming events to a gamepresentation software module executed on gaming machine 61, 62 or 63 tocontrol the play of a game of chance, to control the play of a bonusgame of chance, to control the play of an trajectory-based game or tocontrol the play of an trajectory-based bonus game presented on gamingmachines 61, 62 and 63. As another example, the gaming machines 61, 62and 63 may send gaming events to one another via network connection 71to control the play of the shared trajectory-based bonus game playedsimultaneously on the different gaming machines.

As described with respect to FIG. 7, progressive jackpots may be awardedas part of an trajectory-based game. The progressive jackpots may befunded by groups of gaming machines of various sizes. For example, agroup of gaming machines connected together in a casino may fund aprogressive jackpot in a trajectory-based game. As another example,gaming machines distributed over many gaming properties may be used tofund a progressive jackpot in an trajectory-based game.

In FIG. 11, an trajectory-based game progressive server 82 is connectedto gaming machine 61, 62 and 63 and the remote gaming machine 64 and 64via a wide area progressive network 81. The trajectory-based gameprogressive server 82 may also contain a trajectory-based gamecontroller and provide trajectory-based games to the gaming machines incommunication with the trajectory-based game progressive server. Aportion of the participation fees for trajectory-based games played atthe gaming machines in communication with the trajectory-based gameprogressive server 82 may be used to fund a progressive jackpot. Theamount of the trajectory-based game progressive jackpot may becontinually updated by the trajectory-based game progressive server.Further, the amount of the trajectory-based game progressive jackpot maybe displayed on the gaming machines in communication withtrajectory-based game progressive server or may be displayed on adisplay device near the gaming machines.

Although the foregoing invention has been described in some detail forpurposes of clarity of understanding, it will be apparent that certainchanges and modifications may be practiced within the scope of theappended claims. For instance, while the gaming machines of thisinvention have been depicted as having a display screen physicallyviewed through a vertical glass panel attached to a main gaming machinecabinet, the use of gaming devices in accordance with this invention isnot so limited. For example, the display screen features may be providedon a table top gaming machine where the display screen is viewed througha horizontal glass panel.

1. A method of generating a pay-table for a trajectory-based game ofchance, the method comprising: inserting a plurality of 3-D game objectsinto a 3-D gaming environment wherein each of the plurality of 3-D gameobjects is assigned an initial state; generating a trajectory for eachof the 3-D game objects in the 3-D gaming environment, the trajectory ofeach 3-D game object comprising: the initial state in the 3-D gamingenvironment, a final state in the 3-D gaming environment, and one ormore states in the 3-D gaming environment between the initial state andthe final state; assigning a game outcome for the trajectory-based gameof chance from a set of game outcomes to an aspect of the trajectory foreach 3-D game object; and generating a pay table that relates each gameoutcome in the set of game outcomes to a probability of that gameoutcome occurring in the trajectory-based game of chance.
 2. The methodof claim 1, further comprising: installing the paytable on a gamingmachine and generating game outcomes for a plurality of trajectory-basedgames of chance using the paytable.
 3. The method of claim 1, furthercomprising: generating a set of game outcomes.
 4. The method of claim 1,further comprising: generating a trajectory table that relates each gameoutcome in the set of game outcomes to one or more different initialstates wherein each of the one or more different initial states is forgenerating a trajectory corresponding to its related game outcome. 5.The method of claim 4, further comprising: installing the paytable, the3-D gaming environment and the trajectory table on a gaming machine; onthe gaming machine, generating a first game outcome using the pay table;selecting an initial state for the first game outcome using thetrajectory table; and generating in the 3-D gaming environment a firsttrajectory corresponding to the first game outcome using the initialstate selected from the trajectory table.
 6. The method of claim 1,further comprising: generating the 3-D gaming environment for thetrajectory-based game of chance.
 7. The method of claim 6, wherein the3-D gaming environment comprises data and/or instructions forgenerating; a plurality of 3-D objects; a plurality of trajectory rulesfor determining the trajectory of a moving 3-D object in the 3-D gamingenvironment; a plurality of collision rules for determining effects of acollision between 3-D objects in the 3-D gaming environment; and aplurality of exit rules for removing the 3-D game object from the 3-Dgaming environment.
 8. The method of claim 1, wherein the initial statecomprises an initial position and an initial velocity.
 9. The method ofclaim 1, wherein the trajectory for each of the 3-D game objects isplanar.
 10. The method of claim 1, wherein the trajectory-based game ofchance is a pachinko game.
 11. The method of claim 1, wherein the 3-Dgame object is a sphere.
 12. The method of claim 1, wherein the 3-D gameobject is a polyhedron.
 13. A method of generating a game outcomepresentation in a trajectory-based game of chance, the methodcomprising: along a trajectory of a 3-D game object in a 3-D gamingenvironment wherein the trajectory comprises a sequence of states of the3-D game object in the 3-D gaming environment and wherein each statescomprises at least a position and a velocity of the 3-D game object;generating a first state in the sequence of states of the 3-D gameobject along its trajectory; and generating a second state in thesequence of states of the 3-D game object along its trajectory that isrelated to the first state by a plurality of trajectory rules; whereinone or more two-dimensional images are rendered of the 3-D game objectalong its trajectory in the 3-D gaming environment as part of the gameoutcome presentation for the trajectory-based game of chance.
 14. Themethod of claim 13, further comprising: determining a game outcome forthe trajectory-based game of chance; looking up in an initial positionand an initial velocity of the 3-D game object in a trajectory tablethat corresponds to the determined game outcome and assigning theinitial position and the initial position of the 3-D game object to thefirst state.
 15. The method of claim 13, further comprising: aftergenerating a position and a velocity of the 3-D game object at thesecond state, assigning the position and the velocity of the 3-D gameobject at the second state to the first state and generating a newsecond state.
 16. The method of claim 13, further comprising:determining that the 3-D game object has exited the 3-D gamingenvironment between the first state and the second state; removing the3-D game object from the 3-D gaming environment; and displaying the gameoutcome for the 3-D game object.
 17. The method of claim 13, furthercomprising: detecting an intersection of the 3-D game object with asurface in the 3-D gaming environment between the first state and thesecond state.
 18. The method of claim 17, further comprising: inresponse to detecting the intersection, terminating the trajectory ofthe 3-D game object and removing the 3-D game object from the 3-D gamingenvironment.
 19. The method of claim 17, further comprising: in responseto detecting the intersection, generating a new position for the secondstate different from the position of the second state wherein the 3-Dgame object appears to move discontinuously from the first state to thesecond state.
 20. The method of claim 19, wherein the new position islocated in a bonus area of the 3-D gaming environment.
 21. The method ofclaim 17, further comprising: in response to detecting the intersection,modifying a property of the 3-D game object.
 22. The method of claim 21,wherein the property of the 3-D game object that is modified is selectedfrom the group consisting of a mass property, a geometry property, agraphical rendering property, a sound property and a bonus property. 23.The method of claim 17, further comprising in response to detecting theintersection, modifying a property of an object in the 3-D gamingenvironment.
 24. The method of claim 17, further comprising: in responseto detecting the intersection, triggering a bonus game.
 25. The methodof claim 17, further comprising: in response to detecting theintersection, triggering a game event.
 26. The method of claim 17,further comprising: in response to detecting the intersection, splittingthe 3-D game object into a plurality of 3-D game objects.
 27. The methodof claim 17, further comprising: in response to detecting theintersection, modifying a velocity component of the 3-D game object. 28.The method of claim 27, wherein the velocity component is selected fromthe group consisting of a translational velocity component, a rotationalvelocity component and a vibrational velocity component.
 29. The methodof claim 17, further comprising: in response to detecting theintersection, changing a solidity of an object.
 30. The method of claim17, further comprising: in response to detecting the intersection,changing a visibility of an object.
 31. The method of claim 17, furthercomprising: in response to detecting the intersection, inserting one ormore objects into the gaming environment.
 32. The method of claim 17,further comprising: in response to detecting the intersection, creatingan opening in the gaming environment.
 33. The method of claim 17,further comprising: in response to detecting the intersection, removingan opening in the gaming environment.
 34. The method of claim 17,further comprising: in response to detecting the intersection, changinga size of an object.
 35. The method of claim 17, further comprising: inresponse to detecting the intersection, changing a size of an opening.36. The method of claim 13, further comprising: detecting a collisionbetween the 3-D game object and a second object in the 3-D gamingenvironment between the first state and the second state.
 37. The methodof claim 36, further comprising: in response to detecting the collision,generating an pre-collision state for the 3-D game object and the secondobject; generating a post-collision state for the 3-D game object andthe second object wherein the pre-collision state and the post collisionstate are related by a plurality of collision rules; and assigning thepost-collision state for the 3-D game object to the second state. 38.The method of claim 37, further comprising: generating the plurality ofcollision rules that are used to determine effects of the collisionbetween the 3-D game object and the second game object.
 39. The methodof claim 36, further comprising: in response to detecting the collision,modifying a property of the 3-D game object.
 40. The method of claim 39,wherein the property of the 3-D game object that is modified is selectedfrom the group consisting of a mass property, a geometry property, aphysical property, a graphical rendering property, a sound property anda bonus property.
 41. The method of claim 36, further comprising: inresponse to detecting the collision, modifying a property of the secondobject.
 42. The method of claim 41, wherein the property of the secondobject that is modified is selected from the group consisting of a massproperty, a geometry property, a graphical rendering property, a soundproperty and a bonus property.
 43. The method of claim 36, wherein thesecond object is a second game object.
 44. The method of claim 36,further comprising: in response to detecting the collision, triggering abonus game.
 45. The method of claim 36, further comprising: in responseto detecting the collision, triggering a game event in the trajectorybased game of chance.
 46. The method of claim 36, further comprising: inresponse to detecting the collision, splitting the 3-D game object intoa plurality of 3-D game objects.
 47. The method of claim 36, furthercomprising: in response to detecting the collision, terminating thetrajectory of the 3-D game object and removing the 3-D game object fromthe 3-D gaming environment.
 48. The method of claim 36, furthercomprising: in response to detecting the collision, absorbing all or aportion of the second game object into the 3-D game object.
 49. Themethod of claim 36, further comprising: in response to detecting thecollision changing a solidity of an object.
 50. The method of claim 36,further comprising: in response to detecting the collision, changing avisibility of an object.
 51. The method of claim 36, further comprising:in response to detecting the collision, inserting one or more objectsinto the gaming environment.
 52. The method of claim 36, furthercomprising: in response to detecting the collision, creating an openingin the gaming environment.
 53. The method of claim 36, furthercomprising: in response to detecting the collision, removing an openingin the gaming environment.
 54. The method of claim 36, furthercomprising: in response to detecting the collision, changing a size ofan object.
 55. The method of claim 36, further comprising: in responseto detecting the collision, changing a size of an opening.
 56. Themethod of claim 13, further comprising: determining the plurality oftrajectory rules that are used to relate the first state to the secondstate.
 57. The method of claim 13, wherein the trajectory rules simulateone or more of gravitational forces, frictional forces and environmentalforces on the 3-D game object.
 58. The method of claim 13, wherein thevelocity of the 3-D game object along its trajectory is planar.
 59. Themethod of claim 13, wherein the velocity of the 3-D game object alongits trajectory comprises one or more of translational velocitycomponents, rotational velocity components, vibrational velocitycomponents and combinations thereof.
 60. The method of claim 13, whereinthe plurality of trajectory rules are generated at each location in the3-D gaming environment.
 61. The method of claim 60, wherein a pluralityof trajectory rules at a first location in the 3-D gaming environmentare different than a plurality of trajectory rules at a second locationin the 3-D gaming environment.
 62. The method of claim 13, wherein thetrajectory-based game of chance is a pachinko game.
 63. The method ofclaim 13, wherein the 3-D game object is a sphere.
 64. The method ofclaim 13, wherein the 3-D game object is a polyhedron.